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Calderón Projector for the Hessian of the perturbed Chern–Simons function on a 3-manifold with boundary

Published online by Cambridge University Press:  30 June 2004

Benjamin Himpel ,
Paul Kirk  and
Matthias Lesch
Benjamin Himpel
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA. E-mail: [email protected]
Paul Kirk
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA. E-mail: [email protected]
Matthias Lesch
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86–90, D–50931 Köln, Germany. E-mail: [email protected]
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Abstract

The existence and continuity for the Calderón projector of the perturbed odd signature operator on a 3-manifold is established. As an application we give a new proof of a result of Taubes relating the modulo 2 spectral flow of a family of operators on a homology 3-sphere with the difference in local intersection numbers of the character varieties coming from a Heegard decomposition.

Keywords

Calderón projectorChern–Simons functionHessian57M27 (primary)58J32 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 89 , Issue 1 , July 2004 , pp. 241 - 272
Copyright
2004 London Mathematical Society

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Footnotes

The second named author gratefully acknowledges the support of the National Science Foundation under grant no. DMS-0202148.