Related papers: Geometric structures on orbifolds and holonomy rep…

Let V be a representation space of a finite group G. We determine the group structure of the first homology of the equivariant diffeomorphism group of V. Then we can apply it to the calculation of the first homology of the corresponding…

We develop a generalized covering space theory for a class of uniform spaces called coverable spaces. Coverable spaces include all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular…

Let $\Sigma$ be a surface with either boundary or marked points, equipped with an arbitrary framing. In this note we determine the action of the associated "framed mapping class group" on the homology of $\Sigma$ relative to its boundary…

If G is a (connected) complex Lie Group and Z is a generalized flag manifold for G, the the open orbits D of a (connected) real form G_0 of G form an interesting class of complex homogeneous spaces, which play an important role in the…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

For a topological group $G$ let $E_{\textsf{com}}(G)$ be the total space of the universal transitionally commutative principal $G$-bundle as defined by Adem--Cohen--Torres-Giese. So far this space has been most studied in the case of…

Given a compact Lie group $G$, a reconstruction theorem for free $G$-manifolds is proved. As a by-product reconstruction results for locally trivial bundles are presented. Next, the main theorem is generalized to $G$-manifolds with one…

This paper identifies the homotopy theories of topological stacks and orbispaces with unstable global homotopy theory. At the same time, we provide a new perspective by interpreting it as the homotopy theory of `spaces with an action of the…

Generalised spin structures, or r-spin structures, on a 2-dimensional orbifold \Sigma are r-fold fibrewise connected coverings (also called r-th roots) of its unit tangent bundle ST\Sigma. We investigate such structures on hyperbolic…

For an orbifold X which is the quotient of a manifold Y by a finite group G we construct a noncommutative ring with an action of G such that the orbifold cohomology of X as defined in math.AG/0004129 by Chen and Ruan is the G invariant…

The group of continuous binary operations on a topological space is studied; its relationship with the group of homeomorphisms is established. The category of binary $G$-spaces and bi-equivariant maps is constructed, which is a natural…

Let $G$ be a group of homeomorphisms of a topological space $X$. $G$ is $\textit{(properly) isometrizable}$ if there exists a $G$-invariant (proper) gauge structure on $X$. $G$ is $\textit{equiregular}$ if for every $x \in X$ and every open…

A space of pseudoquotients $\mathcal{B}(X,S)$ is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of injective maps from $X$ to $X$, and…

Let G be a complex reductive linear algebraic group and let K be a maximal compact subgroup of G. Given a nilpotent group \Gamma generated by r elements, we consider the representation spaces Hom(\Gamma,G) and Hom(\Gamma,K) with the natural…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

An important theorem of Ling states that if $G$ is any factorizable non-fixing group of homeomorphisms of a paracompact space then its commutator subgroup $[G,G]$ is perfect. This paper is devoted to further studies on the algebraic…

For two not necessarily commutative topological groups G and T, let H(G,T) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G,T) is a…

Sormani and Wei proved in 2004 that a compact geodesic space has a categorical universal cover if and only if its covering/critical spectrum is finite. We add to this several equivalent conditions pertaining to the geometry and topology of…

Let $P$ be a compact hyperbolic Coxeter truncation polytope of dimension $d\ge 3$, and let $\Gamma$ be the orbifold fundamental group of the associated Coxeter orbifold $\mathcal{O}_P$. Let $\mathscr{G}(\Gamma,G)$ be the geometric component…

A global representation is a compatible collection of representations of the outer automorphism groups of the groups belonging to some collection of finite groups $\mathscr{U}$. Global representations assemble into an abelian category…