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dc.contributor.authorHochs, P.-
dc.contributor.authorWang, B.L.-
dc.contributor.authorWang, H.-
dc.identifier.citationMathematische Zeitschrift, 2022; 301(2):1333-1367-
dc.descriptionPublished online: 17 January 2022-
dc.description.abstractConsider a proper, isometric action by a unimodular locally compact group G on a Riemannian manifold M with boundary, such that M/G is compact. Then an equivariant Dirac-type operator D on M under a suitable boundary condition has an equivariant index index(G)(D) in the K-theory of the reduced group C-algebra C*(r)G of G. This is a common generalisation of the Baum–Connes analytic assembly map and the (equivariant) Atiyah–Patodi–Singer index. In part I of this series, a numerical index index(g)(D) was defined for an element g ∈ G, in terms of a parametrix of D and a trace associated to (g). An Atiyah–Patodi–Singer type index formula was obtained for this index. In this paper, we show that, under certain conditions, Τ(g)(index(G)(D))=index(g)(D), for a trace τ(g) defined by the orbital integral over the conjugacy class of g. This implies that the index theorem from part I yields information about the K-theoretic index index(G)(D). It also shows that index(G)(D) is a homotopy-invariant quantity-
dc.description.statementofresponsibilityPeter Hochs, Bai-Ling Wang, Hang Wang-
dc.rights© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
dc.titleAn equivariant Atiyah–Patodi–Singer index theorem for proper actions II: the K-theoretic index-
dc.typeJournal article-
dc.identifier.orcidHochs, P. [0000-0001-9232-2936]-
Appears in Collections:Mathematical Sciences publications

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