Related papers: An Equivariant Generalization of McDuff's Theorem

Let M be an open, connected manifold. A classical theorem of McDuff and Segal states that the sequence of configuration spaces of n unordered, distinct points in M is homologically stable with coefficients in Z: in each degree, the integral…

We develop the concept of twisted ambidexterity in a parametrized presentably symmetric monoidal $\infty$-category, which generalizes the notion of ambidexterity by Hopkins and Lurie and the Wirthm\"uller isomorphisms in equivariant stable…

In 1998, Goresky, Kottwitz, and MacPherson showed that for certain projective varieties X equipped with an algebraic action of a complex torus T, the equivariant cohomology ring H_T(X) can be described by combinatorial data obtained from…

For discrete groups G, we introduce equivariant Nielsen invariants. They are equivariant analogs of the Nielsen number and give lower bounds for the number of fixed point orbits in the G-homotopy class of an equivariant endomorphism f:X->X.…

For a discrete poset $\mathcal X$, McCord proved that the natural map $|{\mathcal X}|\to {\mathcal X}$, from the order complex to the poset with the Up topology, is a weak homotopy equivalence. Much later, \u{Z}ivaljevi\'{c} defined the…

We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G-homotopy theory is "pieced together" from the G/U-homotopy theories…

For $G$ a topological group, existence theorems by Milnor (1956), Gelfand-Fuks (1968), and Segal (1975) of classifying spaces for principal $G$-bundles are generalized to $G$-spaces with torsion. Namely, any $G$-space approximately covered…

Steenrod homotopy theory is a framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; from another viewpoint, it studies the topology of the lim^1 functor (for inverse sequences of groups). This…

In the paper \emph{K.~Sigmon} A strong homotopy axiom for Alexander cohomology, Proc. Amer. Math. Soc. \textbf{31:1} (1972), 271--275 it was proven that if $G$ is compact topological group or field then in the Homotopy Axiom for…

This paper proves that the two homotopy theories for orbispaces given by Gepner and Henriques and by Schwede, respectively, agree by providing a zig-zag of Dwyer-Kan equivalences between the respective topologically enriched index…

Let X be a complex projective variety of dimension n with only isolated normal singularities. In this paper we prove, using mixed Hodge theory, that if the link of each singular point of X is (n-2)-connected, then X is a formal topological…

For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivariant $E$-theory of the $C^*$-algebra of…

Suppose one is given a discrete group G, a cocompact proper G-manifold M, and a G-self-map f of M. Then we introduce the equivariant Lefschetz class of f, which is globally defined in terms of cellular chain complexes, and the local…

Building upon previous works of Proudfoot and Ramos, and using the categorical framework of Sam and Snowden, we extend the weak categorical minor theorem from undirected graphs to quivers. As case of study, we investigate the consequences…

We present a slight variation on a notion of weak \infty-groupoid introduced by Grothendieck in Pursuing Stacks and we study the homotopy theory of these \infty-groupoids. We prove that the obvious definition for homotopy groups of…

Diffeological spaces are generalizations of smooth manifolds. In this paper, we study the homotopy theory of diffeological spaces. We begin by proving basic properties of the smooth homotopy groups that we will need later. Then we introduce…

Kontsevich conjectured that $\text{BDiff}(M, \text{rel }\partial)$ has the homotopy type of a finite CW complex for all compact $3$-manifolds with non-empty boundary. Hatcher-McCullough proved this conjecture when $M$ is irreducible. We…

We prove that the category $\textbf{G-Cat}$ of small categories with $G$-action forms a model of unstable $G$-global homotopy theory for every discrete group $G$, generalizing Schwede's global model structure on $\textbf{Cat}$. As a…

Michael Shub proved in 1969 that the topological conjugacy class of an expanding endomorphism on a compact manifold is determined by its homotopy type. In this article we generalize this result in two directions. In one direction we…

In this paper, we introduce the concepts of m-quasiconvex, originally m-quasiconvex,and generalized m-quasiconvex functionals on topological vector spaces. Then we extend the concept of point separable topological vector spaces (by the…