# American Institute of Mathematical Sciences

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

## Singular spaces and generalized Poincaré complexes

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

Received  March 2009 Revised  August 2009 Published  December 2009

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.
Citation: Markus Banagl. Singular spaces and generalized Poincaré complexes. Electronic Research Announcements, 2009, 16: 63-73. doi: 10.3934/era.2009.16.63
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