A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Homotopy commutativity in quasitoric manifolds depends on polytope structure and characteristic matrix type.
In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This give…
Assume that all spaces and maps are localised at a fixed prime . We study the possibility of generating a universal space from a space which is universal in the category of homotopy associative, homotopy commutative H-spaces in the sense that any map f:X->Y to a homotopy associative, homotopy commutative …
This paper classifies commutativity spaces for 3-manifold groups.
The quaternions are non-commutative. The deviation from commutativity is encapsulated in the commutator of unit quaternions. It is known that the k-th power of the commutator is null-homotopic if and only if k is divisible by 12. The main purpose of this paper is to construct a concrete null-homotopy of the 12-th power…
Authors prove de Rham cohomology of Poisson and Jacobi manifolds is trivial.
Simplified and extended a method for rearranging infinite configurations of cubes.
The paper classifies links up to link-homotopy using claspers.
New tribrackets defined to count link homotopy invariants.
We show that a homotopy equivalence between compact, connected, oriented surfaces with non-empty boundary is homotopic to a homeomorphism if and only if it commutes with the Goldman bracket.
We introduce the (general) homotopy groups of spheres as link invariants for Brunnian-type links through the investigations on the intersection subgroup of the normal closures of the meridians of strongly nonsplittable links. The homotopy groups measure the difference between the intersection subgroup and symmetric com…
New algebraic structures for Hermitian geometry cohomologies.
We describe explicit presentations of all stable and the first nonstable homotopy groups of the unitary groups. In particular, for each n >= 2 we supply n homotopic maps that each represent the (n-1)!-th power of a suitable generator of pi_2n(U(n)) = Z_{n!}. The product of these n commuting maps is the constant map to …
We introduce some chain maps between Khovanov complexes. Each of the chain maps commutes with a chain homotopy map and a retraction maps which obtain a Reidemeister invariance of Khovanov homology.
Study primes dividing torsion in homology of commuting elements in Lie groups.
Study characteristic classes for TC structures on principal G-bundles.
The space of metrics with positive Ricci curvature on spheres has special algebraic structures.
For dimensions n greater than or equal to 3, we show that the space of metrics of positive scalar curvature on the n-sphere is homotopy equivalent to a subspace which takes the form of a H-space with a homotopy commutative, homotopy associative product operation. This product operation is based on the connected sum con…
Being a maximal compact subgroup of SL_nC, SU_n is a deformation retract of the former group. In this note we prove that, for sufficiently large n, there is no retraction of SL_nC to SU_n which preserves commutativity.
Lecture notes on singular foliations, smooth and holomorphic.
New method compares geometric and standard cup products.
A classical theorem due to Quillen (1969) identifies the unitary bordism ring with the Lazard ring, which classifies the universal one-dimensional commutative formal group law. We prove an equivariant generalization of this result by identifying the homotopy theoretic -equivariant unitary bordism ring, in…
We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in terms of modules over a stack of parametrized spectra and in terms of diagrams o…
Let M be a closed, oriented, n -manifold, and LM its free loop space. Chas and Sullivan defined a commutative algebra structure in the homology of LM, and a Lie algebra structure in its equivariant homology. These structures are known as the string topology loop product and string bracket, respectively. In this paper w…
New algebraic structure derived from Kähler manifolds.
Let $\g\_2$ be the Hochschild complex of cochains on $C^\infty(\RM^n)$ and $\g\_1$ be the space of multivector fields on $\RM^n$. In this paper we prove that given any -structure ({\rm i.e.} Gerstenhaber algebra up to homotopy structure) on $\g\_2$, and any -morphism ({\rm i.e.} morphism of co…
The complex of "stable forms" on supermanifolds is studied. Stable forms on are represented by certain Lagrangians of "copaths" (formal systems of equations, which may or may not specify actual surfaces) on . Changes of give rise to stability isomorphisms. The Cartan--de Rham complex made of…
We introduce an invariant of tuples of commutative diffeomorphisms on a 4-manifold using families of Seiberg-Witten equations. This is a generalization of Ruberman's invariant of diffeomorphisms defined using 1-parameter families of Seiberg-Witten equations. Our invariant yields an application to the homotopy groups of…
Algebra Situs is a branch of mathematics which has its roots in Jones' construction of his polynomial invariant of links and Drinfeld's work on quantum groups. It encompasses the theory of quantum invariants of knots and 3-manifolds, algebraic topology based on knots, operads, planar algebras, q-deformations, quantum g…
Let be a closed, connected -manifold. Let $\mtm$ denote the Thom spectrum of its stable normal bundle. A well known theorem of Atiyah states that $\mtm$ is homotopy equivalent to the Spanier-Whitehead dual of with a disjoint basepoint, . This dual can be viewed as the function spectrum, , whe…
Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows one to work without introducing ad hoc spaces, by using the language of differe…
New invariants define the rational and real homotopy types of closed manifolds.
The energy of any representative of a homotopy class of maps from a compact and connected Riemannian manifold with nonnegative Ricci curvature into a complete Riemannian manifold with no conjugate points is bounded below by a constant determined by the asymptotic geometry of the target, with equality if and only …
In a recent paper, the authors proved that no spin foliation on a compact enlargeable manifold with Hausdorff homotopy graph admits a metric of positive scalar curvature on its leaves. This result extends groundbreaking results of Lichnerowicz, Gromov and Lawson, and Connes on the non-existence of metrics of positive s…
This paper upgrades instanton TQFT to infinity-categories for better simplification.
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology of both the commutative and Lie types in computations of the cohomology of the ou…
New algebraic structures on manifolds generalize supergeometry concepts.
Given a closed oriented 3-manifold M, we establish an isomorphism between the Heegaard Floer homology group HF^+(-M) and the embedded contact homology group ECH(M). Starting from an open book decomposition (S,h) of M, we construct a chain map Φ^+ from a Heegaard Floer chain complex associated to (S,h) to an embedded co…
Each element of the commutator subgroup of a group can be represented as a product of commutators. The minimal number of factors in such a product is called the commutator length of the element. The commutator length of a group is defined as the supremum of commutator lengths of elements of its commutator subgroup. We …
Let be either or the one point blow-up $\cp# \bcp$ of $\cp$. In both cases carries a family of symplectic forms $\om_\la$, where $\la > -1$ determines the cohomology class $[\om_\la]$. This paper calculates the rational (co)homology of the group $G_\la$ of symplectomorphisms of $(M,\om_\la)$ as …
Doodles link to commutator identities in a 2-sphere.
Study on deformation cohomology for braided commutative structures.
Examining singularities of commuting vector fields on submanifolds.
Study on infinite-type surfaces shows stable commutator length is continuous and defines open subgroups.
New proof and description of commutator subgroups for free and surface groups.
This research extends Lie algebra actions to singular foliations.
Formulae for non-symmetric connections derived from covariant derivatives.
The paper studies Riemannian metrics on Lie groups with specific commutator subgroups.