Vol. 4, No. 3, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Higher genera for proper actions of Lie groups

Paolo Piazza and Hessel B. Posthuma

Vol. 4 (2019), No. 3, 473–504

Let G be a Lie group with finitely many connected components and let K be a maximal compact subgroup. We assume that G satisfies the rapid decay (RD) property and that GK has a nonpositive sectional curvature. As an example, we can take G to be a connected semisimple Lie group. Let M be a G-proper manifold with compact quotient MG. Building on work by Connes and Moscovici (1990) and Pflaum et al. (2015), we establish index formulae for the C-higher indices of a G-equivariant Dirac-type operator on M. We use these formulae to investigate geometric properties of suitably defined higher genera on M. In particular, we establish the G-homotopy invariance of the higher signatures of a G-proper manifold and the vanishing of the Â-genera of a G-spin G-proper manifold admitting a G-invariant metric of positive scalar curvature.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address 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:

Lie groups, proper actions, group cocycles, van Est isomorphism, cyclic cohomology, $K\mkern-2mu$-theory, index classes, higher indices, higher index formulae, higher signatures, $G$-homotopy invariance, higher genera, positive scalar curvature
Mathematical Subject Classification 2010
Primary: 58J20
Secondary: 19K56, 58J42
Received: 19 June 2018
Revised: 21 February 2019
Accepted: 12 March 2019
Published: 17 December 2019
Paolo Piazza
Dipartimento di Matematica
Università degli Studi di Roma “La Sapienza”
Hessel B. Posthuma
Kortweg–de Vries Institute for Mathematics
University of Amsterdam