Abstract
Topological invariance of the intersection homology of a pseudomanifold without codimension one strata, proven by Goresky and MacPherson, is one of the main features of this homology. This property is true for codimension-dependent perversities with some growth conditions, verifying . King reproves this invariance by associating an intrinsic pseudomanifold to any pseudomanifold . His proof consists of an isomorphism between the associated intersection homologies for any perversity with the same growth conditions verifying .
In this work, we prove a certain topological invariance within the framework of strata-dependent perversities, , which corresponds to the classical topological invariance if is a GM-perversity. We also extend it to the tame intersection homology, a variation of the intersection homology, particularly suited for “large” perversities, if there is no singular strata on becoming regular in . In particular, under the above conditions, the intersection homology and the tame intersection homology are invariant under a refinement of the stratification.
Citation
David Chataur. Martintxo Saralegi-Aranguren. Daniel Tanré. "Intersection homology: General perversities and topological invariance." Illinois J. Math. 63 (1) 127 - 163, June 2019. https://doi.org/10.1215/00192082-7617702
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