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Computing twisted signatures and L-classes of stratified spaces

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Abstract.

 This paper establishes an Atiyah-type characteristic class formula for both the twisted signature and the twisted L-classes of a singular space. The result, in its present form, applies to coefficient systems that satisfy a transversality condition near the singularities. This condition is frequently automatically satisfied, e.g. on supernormal spaces or for local systems arising in certain geometric mapping situations. We obtain applications to stratified maps by combining our formula with the Cappell-Shaneson signature formula.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA. (e-mail: banagl@math.wisc.edu), , , , , , US

    Markus Banagl

  2. Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA. (e-mail: cappell@cims.nyu.edu), , , , , , US

    Sylvain E. Cappell

  3. Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA. (e-mail: shaneson@math.upenn.edu), , , , , , US

    Julius L. Shaneson

Authors
  1. Markus Banagl
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  2. Sylvain E. Cappell
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  3. Julius L. Shaneson
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Additional information

Received: 15 May 2002 / Revised version: 23 September 2002 / Published online: 8 April 2003

Mathematics Subject Classification (2000): 32S50, 32S60, 55N25, 55N33, 55R55, 57N80, 57R20, 57R45, 58A35, 58K10

All authors supported in part by NSF grants.

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Banagl, M., Cappell, S. & Shaneson, J. Computing twisted signatures and L-classes of stratified spaces. Math. Ann. 326, 589–623 (2003). https://doi.org/10.1007/s00208-003-0439-4

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  • DOI: https://doi.org/10.1007/s00208-003-0439-4

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