Related papers: Infinite CW-complexes, Brauer groups and phantom c…

We show that there exist infinite-dimensional quasi-flats in the compactly supported Hamiltonian diffeomorphism group of the Liouville domain, with respect to the spectral norm, if and only if the symplectic cohomology of this Liouville…

A finite connected CW complex which is a co-H-space is shown to have the homotopy type of a wedge of a bunch of circles and a simply-connected finite complex after almost $p$-completion at a prime $p$.

We give a new proof of the theorem stating that for any connected linear algebraic group G over an algebraically closed field k of characteristic 0 and for any closed connected subgroup H of G, the unramified Brauer group of G/H vanishes.

We establish a 6-term left exact sequence, involving Galois cohomology of the base field $\mathbb K$, and the Brauer-Picard groupoid of a fusion category. This generalizes a result of Etingof, Nikshych, and Ostrik to the setting where…

In this paper we propose a new treatment about infinite dimensional manifolds, using the language of category and functor. Our definition of infinite dimensional manifolds is a natural generalization of finite dimensional manifolds in the…

For a compact Lie group G we define a regularized version of the Dolbeault cohomology of a G-equivariant holomorphic vector bundles over non-compact Kahler manifolds. The new cohomology is infinite-dimensional, but as a representation of G…

In this article, we construct a natural group homomorphism $$ \psi: \text{Br}(f)\to H^{1}_{et}(S, f_{*}\mathcal{O}_{X}^{\times}/\mathcal{O}_{S}^{\times})$$ for a faithful affine map $f: X \to S$ of noetherian schemes. Here $\text{Br}(f)$…

Let $Conf^{lf}_{\infty}(\C)$ and $C^{lf}_{\infty}(\C)$ denote the locally finite infinite ordered and unordered configuration spaces of the complex plane. We prove that both $Conf^{lf}_{\infty}(\C)$ and $C^{lf}_{\infty}(\C)$ are aspherical.…

A strict monoidal category referred to as affine Brauer category $\mathcal{AB}$ is introduced over a commutative ring $\kappa$ containing multiplicative identity $1$ and invertible element $2$. We prove that morphism spaces in…

The class of loop spaces whose mod p cohomology is Noetherian is much larger than the class of p-compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg-Mac Lane spaces such as the infinite complex…

Given pointed $CW$-complexes $X$ and $Y$, $\rmph(X, Y)$ denotes the set of homotopy classes of phantom maps from $X$ to $Y$ and $\rmsph(X, Y)$ denotes the subset of $\rmph(X, Y)$ consisting of homotopy classes of special phantom maps. In a…

Let $Y=\Gamma\backslash H^n$ be a quotient of the hyperbolic space by the action of a discrete convex-cocompact group of isometries. We describe certain spaces of $\Gamma$-invariant currents on the sphere at infinity of $H^n$ with support…

Using the structure of the Boson-Fermion Fock space and an argument taken from [2], we give a new proof of the triviality of the $L^2$ cohomology groups on an abstract Wiener space, alternative to that given by Shigekawa [9]. We apply some…

We classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair…

We study the existence of essential phantom maps into co-H-spaces, motivated by Iriye's observation that every suspension space $Y$ of finite type with $H_i(Y;\QQ)\neq 0$ for some $i>1$ is the target of essential phantom maps. We show that…

We study the finite generation of homotopy groups of closed manifolds and finite CW-complexes by relating it to the cohomology of their fundamental groups. Our main theorems are as follows: when $X$ is a finite CW-complex of dimension $n$…

The computation of the Brauer group BM of modified supergroup algebras is perfomed, yielding, in particular, the computation of the Brauer group of all finite-dimensional triangular Hopf algebras when the base field is algebraically closed…

In a previous article, we introduced notions of finiteness obstruction, Euler characteristic, and L^2-Euler characteristic for wide classes of categories. In this sequel, we prove the compatibility of those notions with homotopy colimits of…

A category of Brauer diagrams, analogous to Turaev's tangle category, is introduced, and a presentation of the category is given; specifically, we prove that seven relations among its four generating homomorphisms suffice to deduce all…

We expand Topological Field Theory on some special CW-complexes (brane complexes). This Brane Topological Field Theory one-to-one corresponds to infinite dimensional Frobenius Algebras, graduated by CW-complexes of lesser dimension. We…