Intersection Cohomology

Volume 50 of the series Progress in Mathematics pp 221-233

Problems and Bibliography on Intersection Homology

  • M. GoreskyAffiliated withDepartment of Mathematics, Northeastern University
  • , R. MacPhersonAffiliated withDepartment of Mathematics, Brown University

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Before considering various possible extensions of intersection homology (such as intersection K-theory), we wish to reflect on small resolutions[D], [F]. For a small resolution π: \( \tilde X \to X \) there is a canonical isomorphism \( H_* (\tilde X) \cong IH_* (X) \). We might expect other “intersection functors” to satisfy a similar identity. A severe limitation on the existence of such functors is therefore provided by the existence of spaces which have two different small resolutions.