This article is available for purchase or by subscription. See below.
Abstract
|
Let
be a finitely connected Lie
group and let
be a maximal
compact subgroup. Let
be a cocompact
-proper
manifold with boundary, endowed with a
-invariant
metric which is of product type near the boundary. Under additional assumptions on
,
for example that it satisfies the rapid decay condition and is such that
has nonpositive sectional curvature, we define higher Atiyah–Patodi–Singer
-indices associated
to elements
and to a
generalized
-equivariant
Dirac operator
on
with
-invertible boundary
operator
.
We then establish a higher index formula for these
-indices
and use it in order to introduce higher genera for
,
thus generalizing to manifolds with boundary the results that we have
established in Part I. Our results apply in particular to a semisimple Lie group
. We use
crucially the pairing between suitable relative cyclic cohomology groups and relative
-theory
groups.
|
PDF Access Denied
However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/akt
We have not been able to recognize your IP address
44.201.96.43
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
Atiyah–Patodi–Singer higher index theory, higher indices,
$K\mkern-2mu$-theory, cyclic cohomology, Lie groups, proper
actions, noncommutative geometry, groupoids, group
cocycles, delocalized cocycles, index classes, relative
pairing, excision
|
Mathematical Subject Classification
Primary: 58J20
Secondary: 19K56, 58J22, 58J42
|
Milestones
Received: 1 February 2021
Revised: 1 June 2021
Accepted: 21 June 2021
Published: 12 February 2022
|
|