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Intersection homology Künneth theorems

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Abstract

Cohen, Goresky, and Ji showed that there is a Künneth theorem relating the intersection homology groups \({I^{\bar p}H_*(X\times Y)}\) to \({I^{\bar p}H_*(X)}\) and \({I^{\bar p}H_*(Y)}\) , provided that the perversity \({\bar p}\) satisfies rather strict conditions. We consider biperversities and prove that there is a Künneth theorem relating \({I^{\bar p,\bar q}H_*(X\times Y)}\) to \({I^{\bar p}H_*(X)}\) and \({I^{\bar q}H_*(Y)}\) for all choices of \({\bar p}\) and \({\bar q}\) . Furthermore, we prove that the Künneth theorem still holds when the biperversity p, q is “loosened” a little, and using this we recover the Künneth theorem of Cohen–Goresky–Ji.

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  1. Texas Christian University, Fort Worth, TX, USA

    Greg Friedman

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  1. Greg Friedman
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Friedman, G. Intersection homology Künneth theorems. Math. Ann. 343, 371–395 (2009). https://doi.org/10.1007/s00208-008-0275-7

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  • DOI: https://doi.org/10.1007/s00208-008-0275-7

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