Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant embedding theorems and topological index maps   The construction of topological index maps for equivariant families of Dirac
operators requires factoring a general smooth map through maps of a very simple
type: zero sections of vector bundles, open embeddings, and vector bundle
projections. Roughly speaking, a normally non-singular map is a map together
with such a factorisation. These factorisations are models for the topological
index map. Under some assumptions concerning the existence of equivariant
vector bundles, any smooth map admits a normal factorisation, and two such
factorisations are unique up to a certain notion of equivalence. To prove this,
we generalise the Mostow Embedding Theorem to spaces equipped with proper
groupoid actions. We also discuss orientations of normally non-singular maps
with respect to a cohomology theory and show that oriented normally
non-singular maps induce wrong-way maps on the chosen cohomology theory. For
K-oriented normally non-singular maps, we also get a functor to Kasparov's
equivariant KK-theory. We interpret this functor as a topological index map.

22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas