Related papers: Equivariant embedding theorems and topological ind…

For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results…

Expanding on the comprehensive factorization of functors internal to a category C, under fairly mild conditions on a monad T on C we establish that this orthogonal factorization system exists even in Burroni's category Cat(T) of (internal)…

Given a generic PL map or a generic smooth fold map $f:N^n\to M^m$, where $m\ge n$ and $2(m+k)\ge 3(n+1)$, we prove that $f$ lifts to a PL or smooth embedding $N\to M\times\mathbb R^k$ if and only if its double point locus $\{(x,y)\in…

We describe the Chow homology and cohomology of toric variety bundles, with no restrictions on the singularities of the fibre. We present the ordinary and equivariant homologies as modules over the cohomology of the base, identify the…

We construct a comparison map from the topological K-theory of the dg-category of twisted perfect complexes on certain global quotient stacks to twisted equivariant K-theory, generalizing constructions of Halpern-Leistner-Pomerleano and…

The purpose of this note is to observe that a homomorphism of discrete groups $f:\Gamma\to G$ arises as the induced map $\pi_0(\mathfrak{M})\to \pi_0(\mathfrak{X})$ on path components of some closed normal inclusion of topological groups…

The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map.…

We study equivariant linear maps between finite-dimensional matrix algebras, as introduced by Bhat. These maps satisfy an algebraic property which makes it easy to study their positivity or k-positivity. They are therefore particularly…

Let $K$ be a $k$-dimensional simplicial complex having $n$ faces of dimension $k$, and $M$ a closed $(k-1)$-connected PL $2k$-dimensional manifold. We prove that for $k\ge3$ odd $K$ embeds into $M$ if and only if there are $\bullet$ a…

For any compact Lie group $G$ and any $n$ we construct a smooth $G$-manifold $U_n(G)$ such that any smooth $n$-dimensional $G$-manifold can be embedded in $U_n(G)$ with a trivial normal bundle. Furthermore, we show that such embeddings are…

We introduce the notion of coupled embeddability, defined for maps on products of topological spaces. We use known results for nonsingular biskew and bilinear maps to generate simple examples and nonexamples of coupled embeddings. We study…

A generalisation of the equivariant Dixmier-Douady invariant is constructed as a second-degree cohomology class within a new semi-equivariant \v{C}ech cohomology theory. This invariant obstructs liftings of semi-equivariant principal…

Let $M$ be a symplectic manifold equipped with a Hamiltonian action of a torus $T$. Let $F$ denote the fixed point set of the $T$-action and let $i:F\hookrightarrow M$ denote the inclusion. By a theorem of F. Kirwan \cite{K} the induced map…

In this paper we introduce the notion of cofrontal mappings, as the dual objects to frontal mappings, and study their basic local and global properties. Cofrontals are very special mappings and far from generic nor stable except for the…

Recently the author has introduced cobordism-like modules induced from generic maps whose codimensions are negative. They are generalizations of cobordism modules of manifolds. They have been introduced in generalizing the following theorem…

We introduce a double framing construction for moduli spaces of quiver representations. It allows us to reduce certain sheaf cohomology computations involving the universal representation, to computations involving line bundles, making them…

We study several duality isomorphisms between equivariant bivariant K-theory groups, generalising Kasparov's first and second Poincare duality isomorphisms. We use the first duality to define an equivariant generalisation of Lefschetz…

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant…

We look at topological equisingularity of a holomorphic family of reduced mapping germs f_t:(C^3,O)->C over a contractible base T having non-isolated singularities, by means of their normalisations. We introduce the notion of…

Let $\varphi\colon\Gamma\to G$ be a homomorphism of groups. We consider factorizations $\Gamma\xrightarrow{f} M\xrightarrow{g} G$ of $\varphi$ such that either $g$ or $f$ are universal normal maps (namely, crossed modules). These two…