Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Immersions and the unbounded Kasparov product: embedding spheres into
  Euclidean space   We construct an unbounded representative for the shriek class associated to
the embeddings of spheres into Euclidean space. We equip this unbounded
Kasparov cycle with a connection and compute the unbounded Kasparov product
with the Dirac operator on $\mathbb R^{n+1}$. We find that the resulting
spectral triple for the algebra $C(\mathbb S^n)$ differs from the Dirac
operator on the round sphere by a so-called index cycle, whose class in
$KK_0(\mathbb C, \mathbb C)$ represents the multiplicative unit. At all points
we check that our construction involving the unbounded Kasparov product is
compatible with the bounded Kasparov product using Kucerovsky's criterion and
we thus capture the composition law for the shriek map for these immersions at
the unbounded KK-theoretical level.

0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio