Related papers: Whitehead torsion of inertial h-cobordisms
This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…
This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…
We consider the topological category of $h$-cobordisms between manifolds with boundary and compare its homotopy type with the standard $h$-cobordism space of a compact smooth manifold.
We study a non-pointed version of the notion of torsion theory in the framework of categories equipped with a posetal monocoreflective subcategory such that the coreflector inverts monomorphisms. We explore the connections of such torsion…
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.
In this paper we define a new cohomology theory for a $B$-algebra $A$. We use this cohomology to study deformations of algebras $A[[t]]$, that have a $B$-algebra structure.
Extensive and systematic machine computations are carried out to investigate the integral cohomology of the Euclidean Bianchi groups and their congruence subgroups. The collected data give insight on several aspects, including the…
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described. A suspended copy of the cokernel-of-J spectrum…
In a group, a generalized torsion element is a non-identity element whose some non-empty finite product of its conjugates yields the identity. Such an element is an obstruction for a group to be bi-orderable. We show that the Weeks…
We study fundamental groups of clique complexes associated to random graphs. We establish thresholds for their cohomological and geometric dimension and torsion. We also show that in certain regime any aspherical subcomplex of a random…
We describe the equivariant cobordism ring of smooth toric varieties. This equivariant description is used to compute the ordinary cobordism ring of such varieties.
We introduce and study the category of Hodge microsheaves which is a Hodge-version of the category of microsheaves for a certain class of holomorphic exact symplectic manifolds. We then study Hodge-theoretic version of wrapped sheaves and…
We define and study binary operations for homotopy groups with coefficients. We give conditions to prove that certain binary operations are the homomorphic image of the generalized Whitehead product. This allows carrying over properties of…
We study the behaviors of quantum groups under an edge contraction. We show that there exists an explicit embedding induced by an edge contraction operation. We further conjecture that this explicit embedding is a section of an explicit…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
We study the divisor of the Reidemeister torsion on the variety of irreducible ${\rm SL}_2\mathbb{C}$-characters of certain knots and links, and provide a geometric interpretation of them. We focus in particular on the family of odd-twisted…
Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…