Related papers: Genuine equivariant factorization homology

We give an account of the theory of factorization spaces, categories, functors, and algebras, following the approach of [Ras1]. We apply these results to give geometric constructions of factorization $\mathbb{E}_n$ algebras describing mixed…

Given a spin rational homology sphere $Y$ equipped with a $\mathbb{Z}/m$-action preserving the spin structure, we use the Seiberg--Witten equations to define equivariant refinements of the invariant $\kappa(Y)$ from \cite{Man14}, which take…

The notion of a proper Ellis semigroup compactification is introduced. Ellis's functional approach shows how to obtain them from totally bounded equiuniformities on a phase space $X$ when the acting group $G$ is with the topology of…

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the…

In this work, we study those differential graded algebras (DGAs) that arise from ring spectra through the extension of scalars functor. Namely, we study DGAs whose corresponding Eilenberg-Mac Lane ring spectrum is equivalent to $H\mathbb{Z}…

This is the first in a series of papers, where we introduce and study topological spaces that realize the algebras of quasi-invariants of finite reflection groups. Our result can be viewed as a generalization of a well-known theorem of A.…

This article investigates equivariant parametrized cellular cohomology, a cohomology theory introduced by Costenoble-Waner for spaces with an action by a compact Lie group $G$. The theory extends the $RO(G)$-graded cohomology of a $G$-space…

We show that the $\infty$-category of normed algebras in genuine $G$-spectra, as introduced by Bachmann-Hoyois, is modelled by strictly commutative algebras in $G$-symmetric spectra for any finite group $G$. We moreover provide an analogous…

We give a method for computing factorization homology of $\oper{E}_n$-algebra using as an input an algebraic version of higher Hochschild homology due to Pirashvili. We then show how to compute higher Hochschild homology and cohomology when…

These notes are an expanded version of two series of lectures given at the winter school in mathematical physics at les Houches and at the Vietnamese Institute for Mathematical Sciences. They are an introduction to factorization algebras,…

We consider a notion of exact sequences in any -not necessarily exact- pointed category relative to a given (E;M)-factorization structure. We apply this notion to introduce and investigate a new notion of exact sequences of semimodules over…

In this article, we investigate the category $\mathcal{A}^G$ of equivariant objects of an additive category $\mathcal{A}$ with respect to an action of a finite group $G$. We show that if $G$ is solvable then we can reconstruct $\mathcal{A}$…

Let G be a general (not necessarily finite dimensional compact) Lie group, let g be its Lie algebra, let Cg be the cone on g in the category of differential graded Lie algebras, and consider the functor which assigns to a chain complex V…

Let M be a connected, simply connected, closed and oriented manifold, and G a finite group acting on M by orientation preserving diffeomorphisms. In this paper we show an explicit ring isomorphism between the orbifold string topology of the…

Let $F$ be an affine flat group scheme over a commutative ring $R$, and $S$ an $F$-algebra (an $R$-algebra on which $F$ acts). We define an equivariant analogue $Q_F(S)$ of the total ring of fractions $Q(S)$ of $S$. It is the largest…

We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold $(M,\rg)$. In other words, we establish a canonical isomorphism between the spaces of…

For a finite abelian group $G$, we compute the $G$-equivariant formal group law corresponding to the $G$-equivariant complex cobordism spectrum with its canonical complex orientation.

Let $A \leq G$ be a subgroup of a group $G$. An $A$-complement of $G$ is a subgroup $H$ of $G$ such that $G = A H$ and $A \cap H = \{1\}$. The \emph{classifying complements problem} asks for the description and classification of all…

Let $G$ be an infinite discrete group and let $\underline{E}G$ be a classifying space for proper actions of $G$. Every $G$-equivariant vector bundle over $\underline{E}G$ gives rise to a compatible collection of representations of the…

We consider the semi-direct products $G=\mathbb Z^2\rtimes GL_2(\mathbb Z), \mathbb Z^2\rtimes SL_2(\mathbb Z)$ and $\mathbb Z^2\rtimes\Gamma(2)$ (where $\Gamma(2)$ is the congruence subgroup of level 2). For each of them, we compute both…