New quandle structures found on topological spaces.
problem No nontrivial quandle structures on [0,1].
method Analyzing topological spaces of positive dimension.
result Infinitely many nonisomorphic quandle structures exist.
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48 results for “nontrivial structures”
Found a new connected component in symplectic structures.
problem Understanding symplectic structures in higher dimensions.
method Provided an example in dimension four.
result First example of a nontrivial connected component.
We show that every complete nontrivial gradient Yamabe soliton admits a special global warped product structure with a one-dimensional base. Based on this, we prove a general classification theorem for complete nontrivial locally conformally flat gradient Yamabe solitons.
The paper studies invariant convex sets in representations with nontrivial copolarity.
problem Understanding the face structure of invariant convex sets in representations with nontrivial copolarity.
method Proves that the face structure of an invariant convex set is determined by its intersection with a fat section, and that a face is exposed if and only if the corresponding face of the intersection is exposed.
result The face structure of invariant convex sets is completely determined by their intersections with fat sections, and exposed faces are preserved.
We prove that a nontrivial complete generalized quasi Yamabe gradient soliton (M; g) must be a quasi Yamabe gradient soliton on each connected component of M and that a nontrivial complete locally conformally at generalized quasi Yamabe gradient soliton has a special warped product structure.
We show that a certain involution on the well known homology sphere (the boundary of the Mazur manifold) induces a nontrivial homomorphism on its Heegard-Floer homology groups (recently defined by Ozsvath and Szabo). We discuss a possible application of this to constructing exotic smooth structures on 4-manifolds.
This research classifies deformations of Yang-Baxter operators using cohomology of -Lie algebras.
problem Classifying deformations of Yang-Baxter operators via cohomology of -Lie algebras.
method Introducing a cohomology theory for -ary self-distributive objects, showing natural injections and isomorphisms, and constructing deformation theories.
result The self-distributive deformations classify the Yang-Baxter operator deformations, with nontrivial examples provided.
The flag curvature of the Numata Finsler structures is shown to admit a nontrivial prolongation to the one-dimensional case, revealing an unexpected link with the Schwarzian derivative of the diffeomorphisms associated with these Finsler structures.
Nontrivial Massey products found on compact Kähler manifolds.
problem Understanding the cohomology structure of compact Kähler manifolds.
method Analyzing the bigraded quasi-isomorphism type of forms on compact Kähler manifolds.
result Nontrivial ABC-Massey products exist on compact Kähler manifolds, including on surfaces and higher-dimensional manifolds.
Study on warped product Yamabe solitons with constant fiber curvature.
problem Characterizing nontrivial warped product Yamabe gradient solitons.
method Investigation of warped product manifolds, derivation of scalar curvature estimates.
result Nontrivial warped product Yamabe gradient solitons have constant scalar curvature in the fiber.
This article is mostly a writeup of two talks, the first given in the Besse Seminar at the Ecole Polytechnique in 1998 and the second given at the 2000 International Congress on Differential Geometry in memory of Alfred Gray in Bilbao, Spain. It begins with a discussion of basic geometry of almost complex 6-manifolds. …
A metric projective structure is a manifold equipped with the unparametrised geodesics of some pseudo-Riemannian metric. We make acomprehensive treatment of such structures in the case that there is a projective Weyl curvature nullity condition. The analysis is simplified by a fundamental and canonical 2-tensor invaria…
Persistent elements are ubiquitous in knot groups, especially for hyperbolic knots.
problem Identifying persistent elements in knot groups under Dehn fillings.
method Combining techniques from knot theory and hyperbolic geometry, including Dehn fillings and automorphisms.
result Persistent elements are structurally pervasive in knot groups, not just rare exceptions.
We recently defined invariants of contact 3-manifolds using a version of instanton Floer homology for sutured manifolds. In this paper, we prove that if several contact structures on a 3-manifold are induced by Stein structures on a single 4-manifold with distinct Chern classes modulo torsion then their contact invaria…
We construct a new class of exact solutions describing spacetimes possessing Lie algebroid symmetry. They are described by generic off-diagaonal 5D metrics embedded in bosonic string gravity and possess nontrivial limits to the Einstein gravity. While we focus on nonholonomic vielbein transforms of the Schwarzschild me…
We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kaehler manifold which respects the almost-Kaehler structure to construct a Fedosov-type deformation quantization on this manifold.
In the spirit of Sullivan's paper "Cycles for the Dynamical Study of Foliated Manifolds and Complex Manifolds", existence of a contact structure on a closed manifold is shown to be equivalent to existence of an ample -invariant cone structure with no nontrivial exact structure cycles on the manifold $S^1 \time…
We study the symplectomorphism groups of an arbitrary closed manifold M equipped with a 1-parameter family of symplectic forms with variable cohomology class. We show that the existence of nontrivial elements in , where is a suitable pair of spac…
Characterizes causal structure dominance for latent variables.
problem Determining dominance relations between causal structures with latent variables.
method Complete characterization for three visible variables, partial for four; uses nontrivial inequality constraints.
result Equivalence classes with nontrivial inequality constraints become ubiquitous as the number of visible variables increases.
We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological obstructions for the existence of b-log symplectic structures similar to those in symplectic geometry.
We present infinitely many nonlocal conservation laws, a pair of compatible local Hamiltonian structures and a recursion operator for the equations describing surfaces in three-dimensional space that admit nontrivial deformations which preserve both principal directions and principal curvatures (or, equivalently, the s…
In this article, it is proved that the eigenvalue variety of the exterior of a nontrivial, non-Hopf, Brunnian link in contains a nontrivial component of maximal dimension. This generalises, for Brunnian links, the nontriviality of the -polynomial of a nontrivial knot in .
New configuration space integrals show nontrivial formal smooth structures on 4-manifold bundles.
problem Disproving the 4-dimensional Smale conjecture by constructing nontrivial bundles.
method Defining new configuration space integrals relying on formal smooth structures.
result Discovering a generalized Miller-Morita-Mumford class obstructing formal smooth structures.
Lower bounds on cone density for nontrivial complements in low dimensions.
problem Finding density limits for minimal cones with nontrivial complements.
method Proving lower bounds on cone density for cones of dimensions less than seven with nontrivial complements.
result Established lower bounds on cone density for minimal cones with nontrivial complements in dimensions less than seven.
New nontrivial breathers found for Ricci flow on noncompact manifolds.
problem Perelman's theorem that nontrivial breathers don't exist for closed manifolds.
method Constructing nontrivial expanding breathers in all dimensions for noncompact manifolds.
result Nontrivial breathers found for Ricci flow on noncompact manifolds.
In this paper we present some structural results on the Lie algebras of transitive isometry groups of a general compact homogenous Riemannian manifold with nontrivial Killing vector fields of constant length.
Algorithm converts curves on ribbon surfaces to contact surgery diagrams.
problem Legendrian realization of curves on ribbon surfaces.
method Explicit algorithm to Legendrian realize homologically nontrivial curves.
result Any two Legendrian realizations of the same curve are Legendrian isotopic.
Smooth HP^2 bundle over S^4 with nontrivial A-genus found.
problem Existence of Riemannian metrics with positive sectional curvature.
method Explained existence of a smooth HP^2 bundle over S^4 with nontrivial A-genus.
result Existence of a smooth HP^2 bundle over S^4 with nontrivial A-genus.
The study examines the structure of certain subgroups of quasi-isometry groups of Euclidean spaces, proving their nontriviality and properties.
problem Investigating the algebraic and dynamical structure of certain subgroups of quasi-isometry groups of Euclidean spaces.
method Analyzing the normal subgroups \(H\) and \(H_\alpha\) of \(QI(\mathbb{R}^n)\) and proving their properties.
result The centers of \(QI(\mathbb{R}^n)/H\) and \(QI(\mathbb{R}^n)/H_\alpha\) are trivial, while these quotients admit nontrivial torsion elements.
A surface automorphism is strongly irreducible if every essential simple closed curve in the surface has nontrivial geometric intersection with its image. We show that a three-manifold admits only finitely many inequivalent surface bundle structures with strongly irreducible monodromy.
The natural bundle of almost-complex structures is considered. The action of the pseudogroup of all diffeomorphisms of on the total space is investigated. A nontrivial 1-st order differential invariant of this action is constructed. It is proved that the Nijenhuise tensor of an almost-complex structu…
Motivated by the usefulness of boundaries in the study of hyperbolic and CAT(0) groups, Bestvina introduced a general approach to group boundaries via the notion of a Z-structure on a group G. Several variations on Z-structures have been studied and existence results have been obtained for some very specific classes of…
New Virasoro-like structures for circle diffeomorphisms with breaks.
problem Constructing Virasoro-like extensions for non-smooth diffeomorphisms.
method Explicit construction of central extensions of Lie groupoids and algebroids.
result Explicit nontrivial central extensions of Lie groupoids and algebroids for broken diffeomorphisms.
It was asked by J.Birman, Williams, and L.Rudolph whether nontrivial Lorentz knots have always positive signature. Lorentz knots are examples of positive braids (in our convention they have all crossings negative so they are negative links). It was shown by L.Rudolph that positive braids have positive signature (if the…
The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of imbeddings obtained by blowing up transversal double points in immersions. These cohomol…
Study path geometries with constant torsion and cone structures.
problem Characterizing path geometries with nontrivial torsion.
method Introducing constant torsion, establishing correspondence with cone structures, describing in terms of integrable systems.
result Path geometries with constant torsion correspond to cone structures on homogeneous ruled surfaces.
In this note, we use the recent work of Honda-Kazez-Matic [HKM] to prove that a closed contact 3-manifold admitting a compatible open book decomposition with a nontrivial monodromy which can be presented as a product of left handed Dehn twists is overtwisted.
Study on Kodaira fibrations with nontrivial cohomology, proving properties of their structure.
problem Characterizing Kodaira fibrations with specific cohomology properties.
method Analyzing invariant rational cohomology and properties of holomorphic sections.
result Kodaira fibrations with invariant cohomology admit specific coverings and monodromies.
Study on a specific type of Lie algebras with Kähler and contact properties.
problem Characterizing and classifying transversely Kähler almost contact metric Lie algebras.
method Analyzing properties of Lie algebras with contact forms and Kähler structures, considering center dimensions and quotient properties.
result Classification of 5-dimensional η-Einstein transversely Kähler almost contact metric Lie algebras.
We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S^1 or R into R^n. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb(S^1,R^n) when n is even and greater than 3. …
Almost product structures on statistical manifolds and para-Kähler-like statistical submersionsmath.DG
Study on statistical manifolds with product structures and their properties.
problem Investigating statistical manifolds with almost product structures.
method Proving properties of para-Kähler-like statistical manifolds and deriving properties of statistical submersions compatible with almost product structures.
result The statistical structure of a para-Kähler-like statistical manifold of constant curvature is a Hessian structure.
We show that all nontrivial embeddings of planar graphs on the torus contain a nontrivial knot or a nonsplit link. This is equivalent to showing that no minimally knotted planar spatial graphs on the torus exist that contain neither a nontrivial knot nor a nonsplit link all of whose components are unknots.
We determine when certain state cycles represent nontrivial Khovanov homology classes by analyzing features of the state graph. Using this method, we are able to produce hyperbolic knots with arbitrarily many diagonals containing nontrivial state cycle homology classes. This gives lower bounds on the Khovanov width of …
Study on the topology of ordered disc configurations, revealing nontrivial homotopy classes.
problem Topology of ordered disc configurations and their homotopy types.
method Analysis of ordered configuration spaces of hard discs, focusing on homotopy types and nontrivial classes.
result Exhibit nontrivial classes in π_{n-3} for all n, and their persistence in deformed ambient discs.
In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an abelian group, the conformal cobordism group, which classifies the conformally flat structures according to whether they bound (…
Dunfield-Garoufalidis and Boyer-Zhang proved that the A-polynomial of a nontrivial knot in is nontrivial. In this paper, we use holonomy perturbations to prove the non-triviality of the A-polynomial for a nontrivial, null-homotopic knot in an irreducible 3-manifold. Also, we give a strong constraint on the A-po…
Study shows nontrivial intersections of subgroups on homogeneous spaces.
problem Understanding intersections of subgroups on homogeneous spaces.
method Analyzing reductive subgroups of semisimple Lie groups.
result Finiteness of totally geodesic submanifolds with bounded volume.
This note gives a proof that the -polynomial of any nontrivial knot in has nontrivial -degree.