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Realizing the analytic surgery group of Higson and Roe geometrically part III: higher invariants

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Abstract

We construct an isomorphism between the geometric model and Higson-Roe’s analytic surgery group, reconciling the constructions in the previous papers in the series on “Realizing the analytic surgery group of Higson and Roe geometrically” with their analytic counterparts. Following work of Lott and Wahl, we construct a Chern character on the geometric model for the surgery group; it is a “delocalized Chern character”, from which Lott’s higher delocalized \(\rho \)-invariants can be retrieved. Following work of Piazza and Schick, we construct a geometric map from Stolz’ positive scalar curvature sequence to the geometric model of Higson-Roe’s analytic surgery exact sequence.

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Acknowledgments

The authors wish to express their gratitude towards Karsten Bohlen, Heath Emerson, Nigel Higson, Paolo Piazza, Thomas Schick and Charlotte Wahl for discussions. They also thank the Courant Centre of Göttingen, the Leibniz Universität Hannover, the Graduiertenkolleg 1463 (Analysis, Geometry and String Theory) and Université Blaise Pascal Clermont-Ferrand for facilitating this collaboration.

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Authors and Affiliations

  1. Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Keller 401A, Honolulu, HI, 96822, USA

    Robin J. Deeley

  2. Insitut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Magnus Goffeng

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  1. Robin J. Deeley
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Correspondence to Robin J. Deeley.

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Deeley, R.J., Goffeng, M. Realizing the analytic surgery group of Higson and Roe geometrically part III: higher invariants. Math. Ann. 366, 1513–1559 (2016). https://doi.org/10.1007/s00208-016-1365-6

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  • DOI: https://doi.org/10.1007/s00208-016-1365-6

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