New definition of de Rham spaces changes quotient structure.
problem Traditional de Rham spaces defined using nilpotents.
method Uses infinity nilpotent elements for de Rham spaces.
result De Rham spaces are quotients by germs of diagonals.
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48 results for “infinity nilpotent”
Cohomologie et parabolicitemath.DG
We obtain a topological interpretation for the space of harmonic forms for some complete Riemannian manifold : when the geometry at infinity is the geometry of a simply connected nilpotent Lie group, when the geometry at infinity is a symmetric space with non positive curvature and also when the geometry at infin…
Motivated by families of formal moduli problems, in this note we generalize the notion of L-infinity space by allowing sheaves of L-infinity algebras over any (reasonable) nilpotent dg manifold. We discuss various examples including those coming from Lie algebroids. Given a Lie algebroid, we show that there is an L-inf…
The Deligne groupoid is a functor from nilpotent differential graded Lie algebras concentrated in positive degrees to groupoids; in the special case of Lie algebras over a field of characteristic zero, it gives the associated simply connected Lie group. We generalize the Deligne groupoid to a functor gamma from L-infin…
Higher nilpotent analogues of the -structure are explicitly defined on arbitrary simplicial complexes, generalizing explicit construction of /hep-th/0704.2609. These structures are associated with the higher nilpotent differential , satisfying , which is naturally defined on triangulated manifo…
We give another proof for a result of Brick stating that the simple connectivity at infinity is a geometric property of finitely presented groups. This allows us to define the rate of vanishing of $\p1i$ for those groups which are simply connected at infinity. Further we show that this rate is linear for cocompact latt…
Researchers determine Dehn functions of specific nilpotent groups.
problem Understanding the Dehn functions of central products of nilpotent groups.
method Analyzing families of filiform and Lie groups to determine Dehn functions.
result Confirms conjecture and provides evidence for lower Dehn functions in central products.
A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds. Various operations are explicitly defined on these forms, including exterior derivative and exterior product. The latter one is non-associative. Instead, as ant…
In this paper we consider a canonical compactification of Hitchin's moduli space of stable Higgs bundles with fixed determinant of odd degree over a Riemann surface, producing a projective variety by gluing in a divisor at infinity. We give a detailed study of the compactified space, the divisor at infinity and the mod…
Let G be a finitely generated group with a given word metric. The asymptotic density of elements in G that have a particular property P is defined to be the limit, as r goes to infinity, of the proportion of elements in the ball of radius r which have the property P. We obtain a formula to compute the asymptotic densit…
We study the existence of left invariant closed -structures defining a Ricci soliton metric on simply connected nonabelian nilpotent Lie groups. For each one of these -structures, we show long time existence and uniqueness of solution for the Laplacian flow on the noncompact manifold. Moreover, considering th…
We study a generalization of Hodge structures which first appeared in the work of Cecotti and Vafa. It consists of twistors, that is, holomorphic vector bundles on P^1, with additional structure, a flat connection on C^*, a real subbundle and a pairing. We call these objects TERP-structures. We generalize to TERP-struc…
New non-rigid discrete groups found in hyperbolic spaces.
problem Uniqueness of conformal or spherical CR structures on spheres.
method Nilpotent Sierpiński carpet and stretching to construct non-rigid groups.
result Discrete hyperbolic groups can have non-rigid deformations.
We prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology, over fields of characteristic zero. The key ingredient is the construction of a degree one Hochschild cohomology class on a Floer A-infinity algebra associated to the (k,k)-nilpotent slice Y, ob…
The main aim of this paper is the description of a large class of lattices in some nilpotent Lie groups, sometimes filiformes, carrying a flat left invariant linear connection anf often a left invariant symplectic form. As a consequence we obtain an infinity of, non homeomorphic, compact affine or symplectic manifolds.…
We study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with constant negative curvature. This study uses an interaction between Kähler geometr…
The paper disproves a generalized toral rank conjecture with various counter-examples.
problem The conjecture that the sum of Betti numbers of a compact manifold with a torus action is bounded by .
method Provided counter-examples of smooth nilpotent fibre bundles of nilmanifolds with torus fibres of rank .
result There are sequences of torus fibrations with total space cohomology dimensions converging to 0 as rank increases.
Study on stability of Minkowski spacetime using advanced mathematical techniques.
problem Nonlinear stability of Minkowski spacetime in Einstein vacuum equation.
method Iteration scheme, linearized equation, generalized harmonic gauge, constraint damping, energy and vector field methods, Melrose's b-analysis.
result Polyhomogeneous spacetime metric produced from polyhomogeneous initial data.
Nilpotent quandlesmath.GT
Nilpotent quandles have simple characterizations and are closely related to nilpotency.
problem Characterizing and understanding nilpotent quandles.
method Characterization of generating sets, Hopf property, construction of free nilpotent quandles, simple presentations of associated groups.
result Nilpotent quandles have the Hopf property and are equivalent to reduced peripheral systems.
Nilpotent Lie algebras obtained from ordered sets and quivers are algebraic Ricci solitons.
problem Constructing nilpotent Lie algebras as algebraic Ricci solitons
method Using transitively and antisymmetrically ordered sets (TAOSs) and incidence algebras
result Nilpotent Lie algebras with arbitrarily high degrees of nilpotency are algebraic Ricci solitons
New method constructs nilpotent Lie algebras from quivers.
problem Constructing nilpotent Lie algebras from quivers.
method Using paths within quivers to construct nilpotent Lie algebras.
result Constructs a broad family of Ricci soliton nilmanifolds.
Study knot invariants using automorphism groups of free nilpotent groups.
problem Developing knot invariants using automorphism groups.
method Nilpotently -localization of knot groups and automorphism groups of free nilpotent groups.
result Maps from outer automorphism groups yield knot invariants.
Nilpotent Sasakian manifolds are Heisenberg nilmanifolds.
problem Characterizing Sasakian manifolds with nilpotent fundamental groups.
method Proved diffeomorphism to Heisenberg nilmanifolds.
result Compact aspherical Sasakian manifolds with nilpotent fundamental groups are Heisenberg nilmanifolds.
We exhibit pseudo Riemannian manifolds which are Szabó nilpotent of arbitrary order, or which are Osserman nilpotent of arbitrary order, or which are Ivanov-Petrova nilpotent of order 3.
Classifies complex structures on specific nilpotent Lie algebras.
problem Classifying complex structures on nilpotent Lie algebras with minimal center.
method Classification through algebraic and geometric methods.
result Space of complex structures on specific Lie algebras up to isomorphism.
We compute the characteristic varieties and the Alexander polynomial of a finitely generated nilpotent group. We show that the first characteristic variety may be used to detect nilpotence. We use the Alexander polynomial to deduce that the only torsion-free, finitely generated nilpotent groups with positive deficiency…
Study on invariant structures on 7D nilpotent Lie groups, focusing on Sasaki and K-contact.
problem Existence and classification of invariant Sasaki and K-contact structures on 7D nilpotent Lie groups.
method Analysis of 22 and 25 classes of 7D nilpotent Lie groups for pseudo-Sasaki and K-contact structures, respectively.
result Contact seven-dimensional algebras have nonzero Ricci tensor in contact directions.
This paper classifies Ricci soliton subgroups in a specific type of nilpotent group.
problem Classifying Ricci soliton subgroups in a specific type of nilpotent group.
method Using the properties of nilpotent Iwasawa groups and Lie subgroups.
result Classification of codimension one Lie subgroups of nilpotent Iwasawa groups that are Ricci solitons.
The study classifies nilpotent Lie algebras up to dimension 9.
problem Classifying nilpotent Lie algebras up to equivalence.
method Developed an algorithm to classify nilpotent Lie algebras of dimension up to 9, and determined the number of inequivalent nice bases for dimensions up to 7.
result Any nilpotent Lie algebra of dimension n has at most countably many inequivalent nice bases.
Study limits of adjoint orbits for Lie groups, describing nilpotent orbits.
problem Understanding limits of adjoint orbits for Lie groups.
method Systematic and topological study of limits of continuous families of adjoint orbits for non-compact simple Lie groups.
result Explicit description of nilpotent orbits in terms of Richardson orbits for hyperbolic semisimple elements.
New findings on complex structures in nilpotent Lie algebras and pseudo-Kähler geometry.
problem Classifying complex structures on nilpotent Lie algebras.
method Analysis of Lie algebras in dimensions eight and higher, identifying structures with pseudo-Kähler metrics.
result Identification of pseudo-Kähler nilmanifolds with invariant complex structures, providing counterexamples and topological restrictions.
Completes classification of G2-structures on specific nilpotent Lie groups.
problem Classifying seven-dimensional nilpotent Lie groups with purely coclosed G2-structures.
method Analyzing nilpotent Lie groups of various steps and dimensions.
result Classification of indecomposable 5- and 6-step nilpotent Lie groups.
The paper studies gradings on nilpotent Lie algebras linked to smooth algebraic varieties.
problem Understanding gradings on nilpotent Lie algebras associated with algebraic varieties.
method Analyzing lattice structures in nilpotent Lie groups and their fundamental groups.
result Conditions for a lattice to be the fundamental group of a smooth complex algebraic variety.
This paper completes the classification of certain nilpotent Lie groups with specific geometric structures.
problem Classifying nilpotent Lie groups with purely coclosed G2-structures.
method Analyzing seven-dimensional nilpotent Lie groups of various steps.
result Classification of indecomposable 5- and 6-step nilpotent Lie groups with these structures.
This paper clarifies privileged coordinates and nilpotent approximation for Carnot manifolds.
problem Understanding privileged coordinates and nilpotent approximation for Carnot manifolds.
method Systematic account on privileged coordinates and nilpotent approximation of Carnot manifolds.
result Description of all systems of privileged coordinates and algebraic characterization of nilpotent groups.
Criterion for nilpotent Lie groups to have nilsolitons.
problem Existence of nilsolitons in nilpotent Lie groups.
method Algebraic criterion for nilpotent Lie algebras, proving necessary and sufficient condition for nilsolitons.
result Criterion provides a necessary and sufficient condition for nilpotent Lie groups to admit nilsolitons.
We study complex product structures on nilpotent Lie algebras, establishing some of their main properties, and then we restrict ourselves to 6 dimensions, obtaining the classification of 6-dimensional nilpotent Lie algebras admitting such structures. We prove that any complex structure which forms part of a complex pro…
Study proves equality of LS-category and cohomological dimension for specific group homomorphisms.
problem Proving equality of LS-category and cohomological dimension for specific group homomorphisms.
method Analyzing epimorphisms and homomorphisms between specific types of almost nilpotent and virtually nilpotent groups.
result Equality of LS-category and cohomological dimension for specified group homomorphisms.
Study nilpotent Higgs bundles and Calabi-Yau moduli metrics.
problem Understand nilpotent Higgs bundles and their metrics.
method Algebraic inequality for nilpotent matrices, geometric applications.
result Sharp upper bound of holomorphic sectional curvatures on Calabi-Yau moduli.
This paper classifies strongly nilpotent special multi-flags and their Goursat counterparts.
problem Local classification of strongly nilpotent special multi-flags and Goursat distributions.
method Study of special multi-flags in homogeneous case, focusing on their weights.
result Strongly nilpotent germs of multiflags from different singularity classes are pairwise inequivalent.
Study on pseudo-Hermitian quadratic nilpotent Lie algebras with methods and classifications.
problem Characterizing and classifying pseudo-Hermitian quadratic nilpotent Lie algebras.
method Construction methods and double extension by planes.
result Complete classification of nilpotent quadratic Lie algebras and pseudo-Hermitian metrics up to dimension 8.
This article provides a complete description of the differential Gerstenhaber algebras of all nilpotent complex structures on any real six-dimensional nilpotent algebra. As an application, we classify all pseudo-Kählerian complex structures on six-dimensional nilpotent algebras such that the differential Gerstenhaber a…
Extends Floquet-Bloch theory to nilpotent groups for geometric applications.
problem Asymptotic problems on nilpotent covers of negatively curved manifolds.
method Generalized Floquet-Bloch theory using Malcev completions.
result Branching formula relating finite and infinite-dimensional representations.
Constructs integrable systems for Lie-Poisson structures at nilpotent elements.
problem Integrability of transverse Lie-Poisson structures at nilpotent elements.
method Using the argument shift method to construct families of functions in involution.
result Provides a uniform construction of completely integrable systems for an infinite family of nilpotent elements.
The paper classifies special nilpotent Lie groups with Ricci-flat and Einstein metrics.
problem Finding metrics on nilpotent Lie groups that are both Ricci-flat and Einstein.
method Classification of metrics using a new criterion for diagonal Einstein metrics.
result Classifications of Ricci-flat metrics on nilpotent Lie groups of dimension ≤8.
Gromov proposed an averaged version of the Dehn function and claimed that in many cases it should be subasymptotic to the Dehn function. Using results on random walks in nilpotent groups, we confirm this claim for most nilpotent groups. In particular, if a nilpotent group satisfies the isoperimetric inequality $δ(l)<Cl…
Study finds only complex 2-step nilpotent Lie groups have Killing-Yano forms.
problem Characterizing Lie groups with Killing-Yano forms.
method Analyzing 2-step nilpotent Lie groups and connected graphs.
result Only complex 2-step nilpotent Lie groups have non-degenerate Killing-Yano forms.
Study torsion-free nilpotent fundamental groups of smooth varieties up to rank 7.
problem Characterize fundamental groups of smooth quasi-projective varieties.
method Analyzes fundamental groups of smooth quasi-projective varieties using topological and Lie group theory.
result Determine fundamental groups for smooth quasi-projective varieties up to rank 7.