This article is available for purchase or by subscription. See below.
Abstract
|
Given a codimension one Riemannian embedding of Riemannian
spin-manifolds
we construct
a family
of
unbounded
-cycles
from
to
, each equipped with a connection
and each representing the
shriek class
. We compute
the unbounded product of
with the Dirac operator
on
and show that this represents
the
-theoretic factorization
of the fundamental class
for all
. In
the limit
the product operator admits an asymptotic expansion of the form
where the “divergent”
part
is an index cycle
representing the unit in
and the constant “renormalized” term is the Dirac operator
on
. The
curvature of
is further shown to converge to the square of the mean curvature of
as
.
|
PDF Access Denied
We have not been able to recognize your IP address
3.94.202.151
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
noncommutative geometry, spectral triple, unbounded
product, unbounded KK-theory, Riemannian immersion
|
Mathematical Subject Classification
Primary: 58B34
Secondary: 53C21
|
Milestones
Received: 19 April 2023
Revised: 11 July 2023
Accepted: 3 September 2023
Published: 6 December 2023
|
© 2023 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
|