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The Hirzebruch Signature Theorem for Conical Metrics

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Arbeitstagung Bonn 2013

Part of the book series: Progress in Mathematics ((PM,volume 319))

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Abstract

Exactly 60 years ago the young Fritz Hirzebruch came up with two spectacular theorems [H53, H54] which set the scene for the future development of algebraic geometry and topology.

Dedicated to my friend Fritz Hirzebruch

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Notes

  1. 1.

    This paper is based on a lecture given in Bonn in May 2013 at the Hirzebruch Memorial Conference but it incorporates significant improvements.

  2. 2.

    For β = 1 there is no purely conical region if we take the hemispherical smoothing, but in this case there is no singularity.

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Author information

Authors and Affiliations

  1. School of Mathematics, JCMB, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK

    Michael Atiyah

Authors
  1. Michael Atiyah
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Correspondence to Michael Atiyah .

Editor information

Editors and Affiliations

  1. Max Planck Institute for Mathematics, Bonn, Germany

    Werner Ballmann

  2. Max Planck Institute for Mathematics, Bonn, Germany

    Christian Blohmann

  3. Max Planck Institute for Mathematics, Bonn, Germany

    Gerd Faltings

  4. Max Planck Institute for Mathematics, Bonn, Germany

    Peter Teichner

  5. Max Planck Institute for Mathematics, Bonn, Germany

    Don Zagier

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Atiyah, M. (2016). The Hirzebruch Signature Theorem for Conical Metrics. In: Ballmann, W., Blohmann, C., Faltings, G., Teichner, P., Zagier, D. (eds) Arbeitstagung Bonn 2013. Progress in Mathematics, vol 319. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-43648-7_1

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