Singular spaces and generalized Poincaré complexes

Markus Banagl

doi:10.3934/era.2009.16.63

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2009, Volume 16: 63-73. Doi: 10.3934/era.2009.16.63

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Singular spaces and generalized Poincaré complexes

Markus Banagl^1,

1.
Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 288, 69120 Heidelberg

Received: February 28, 2009

Revised: July 31, 2009

Published: December 2008

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Abstract

We introduce a method that associates to a singular space a CW complex whose ordinary rational homology satisfies Poincaré duality across complementary perversities as in intersection homology. The method is based on a homotopy theoretic process of spatial homology truncation, whose functoriality properties are investigated in detail. The resulting homology theory is not isomorphic to intersection homology and addresses certain questions in type II string theory related to massless D-branes. The two theories satisfy an interchange of third and second plus fourth Betti number for mirror symmetric conifold transitions. Further applications of the new theory to K-theory and symmetric L-theory are indicated.

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Mathematics Subject Classification: Primary: 55N33, 57P10; Secondary: 81T30, 14J32, 55P30, 55S36.

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