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Singular chain intersection homology for traditional and super-perversities. (English) Zbl 1109.55004

Singular chain intersection homology theory is defined and studied, generalizing the work of H. C. King [Topology Appl. 20, 149-160 (1985; Zbl 0568.55003)] and which agrees with the Deligne sheaf intersection homology of Goresky and MacPherson on any topological stratified pseudomanifold with constant or local coefficients and with traditional perversities or superperversities. It is proved that this singular chain model provides the correct sheaf theoretic intersection homology modules for traditional perversities, even on non-compact topological pseudomanifolds.

MSC:

55N33 Intersection homology and cohomology in algebraic topology
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
57N80 Stratifications in topological manifolds
14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)

Citations:

Zbl 0568.55003
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References:

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