Related papers: Ranicki-Weiss assembly and the Steenrod constructi…

We introduce a complete set of combinatorial data that encode the category $2\mathfrak{Cob}$ of all $2$-cobordisms. As an application, we show that the local monoids of $2\mathfrak{Cob}$ do not have finitely axiomatizable equational…

We construct a separable Frobenius monoidal functor from $\mathcal{Z}\big(\mathsf{Vect}_H^{\omega|_H}\big)$ to $\mathcal{Z}\big(\mathsf{Vect}_G^\omega\big)$ for any subgroup $H$ of $G$ which preserves braiding and ribbon structure. As an…

Let $\left( H,R\right) $ be a finite dimensional semisimple and cosemisimple quasi-triangular Hopf algebra over a field $k$. In this paper, we give the structure of irreducible objects of the Yetter-Drinfeld module category ${}…

We show that the Lusternik-Schnirelmann category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the…

Entwined modules over cowreaths in a monoidal category are introduced. They can be identified to coalgebras in an appropriate monoidal category. It is investigated when such coalgebras are Frobenius (resp. separable), and when the forgetful…

We consider the category of comodules over a smash coproduct coalgebra $C\smashco H$. We show that there is a Grothendieck spectral sequence connecting the derived functors of the Hom functors coming from $C\smashco H$-colinear,…

The polyhedral product is a space constructed from a simplicial complex and a collection of pairs of spaces, which is connected with the Stanley Reisner ring of the simplicial complex via cohomology. Generalizing the previous work Grbic and…

We prove the graded braided commutativity of the Hochschild cohomology of $A$ with trivial coefficients, where $A$ is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some…

In arxiv:1602.04254, we have defined polynomial Witt vectors functor from vector spaces over a perfect field $k$ of positive characteristic $p$ to abelian groups. In this paper, we use polynomial Witt vectors to construct a functorial…

We investigate the triviality of compact Ricci solitons under general scalar conditions involving the Weyl tensor. More precisely, we show that a compact Ricci soliton is Einstein if a generic linear combination of divergences of the Weyl…

We construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply-laced quantum group in its adjoint representation. The braid group action in the adjoint representation lifts to an…

In this paper, we construct (many) Kolyvagin systems out of Stickelberger elements, utilizing ideas borrowed from our previous work on Kolyvagin systems of Rubin-Stark elements. We show how to apply this construction to prove results on the…

We classify all groups G and all pairs (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the support of the direct sum of V and W generates G, the square of the braiding between V and W is not the identity, and the Nichols…

Generalizing the notion of a Koszul algebra, a graded k-algebra A is K2 if its Yoneda algebra is generated as an algebra in cohomology degrees 1 and 2. We prove a strong theorem about K2 factor algebras of Koszul algebras and use that…

We prove basic statements about the Hermitian K-theory of exact form categories with weak equivalences. Notably, we extend a quadratic functor with values in abelian groups from an exact category to its category of bounded chain complexes…

We show that for quasi-compact quasi-separated schemes of finite dimension, the constructibility condition in real \'etale cohomology agrees with a notion of constructibility arising naturally from topology. As application we prove that the…

Let S be an essentially smooth scheme over a field and l a prime number invertible on S. We show that the algebra of bistable operations in the mod l motivic cohomology of smooth S-schemes is generated by the motivic Steenrod operations.…

We consider the assembly map for principal bundles with fiber a countable discrete group. We obtain an index-theoretic interpretation of this homomorphism by providing a tensor-product presentation for the module of sections associated to…

Given an arbitrary countably generated rigid C*-tensor category, we construct a fully-faithful bi-involutive strong monoidal functor onto a subcategory of finitely generated projective bimodules over a simple, exact, separable, unital…

This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule…