Transactions of the American Mathematical Society

Author(s): Greg Friedman
Journal: Trans. Amer. Math. Soc. 359 (2007), 1977-2019.
MSC (2000): Primary 55N33; Secondary 32S60, 57N80
Posted: November 22, 2006
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 55N33, 32S60, 57N80

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

DOI: 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
Posted: November 22, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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