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Realizing the analytic surgery group of Higson and Roe geometrically part II: relative \(\eta \)-invariants

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Abstract

We apply the geometric analog of the analytic surgery group of Higson and Roe to the relative \(\eta \)-invariant. In particular, by solving a Baum–Douglas type index problem, we give a “geometric” proof of a result of Keswani regarding the homotopy invariance of relative \(\eta \)-invariants. The starting point for this work is our previous constructions in “Realizing the analytic surgery group of Higson and Roe geometrically, Part I: The geometric model”.

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Notes

  1. For definitions see below in Sect. 2.3.

  2. Compare with Remark 4.3.

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Acknowledgments

The authors wish to express their gratitude towards Heath Emerson, Nigel Higson, and Thomas Schick for discussions. They also thank the Courant Centre of Göttingen, the Leibniz Universität Hannover and the Graduiertenkolleg 1463 (Analysis, Geometry and String Theory) for facilitating this collaboration. The authors also thank the referee for a number of useful suggestions.

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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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  2. Magnus Goffeng
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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 II: relative \(\eta \)-invariants. Math. Ann. 366, 1319–1363 (2016). https://doi.org/10.1007/s00208-016-1364-7

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  • DOI: https://doi.org/10.1007/s00208-016-1364-7

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