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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Singular chain intersection homology for traditional and super-perversities


Author: Greg Friedman
Journal: Trans. Amer. Math. Soc. 359 (2007), 1977-2019
MSC (2000): Primary 55N33; Secondary 32S60, 57N80
Published electronically: November 22, 2006
MathSciNet review: 2276609
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Abstract: We introduce a singular chain intersection homology theory which generalizes that of King and which agrees with the Deligne sheaf intersection homology of Goresky and MacPherson on any topological stratified pseudomanifold, compact or not, with constant or local coefficients, and with traditional perversities or superperversities (those satisfying $ \bar p(2)>0$). For the case $ \bar p(2)=1$, these latter perversities were introduced by Cappell and Shaneson and play a key role in their superduality theorem for embeddings. We further describe the sheafification of this singular chain complex and its adaptability to broader classes of stratified spaces.


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Additional Information

Greg Friedman
Affiliation: Department of Mathematics, Texas Christian University, Box 298900, Fort Worth, Texas 76129

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03962-6
PII: S 0002-9947(06)03962-6
Keywords: Intersection homology, superperversity, singular chain, stratifed space, pseudomanifold, homotopically stratified space, manifold weakly stratified space
Received by editor(s): July 16, 2004
Received by editor(s) in revised form: January 11, 2005
Published electronically: November 22, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.