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On the cohomology of stable map spaces

Kai Behrend·Anne O'Halloran
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Abstract

We describe an approach to calculating the cohomology rings of stable map spaces. The method we use is due to Akildiz-Carrell and employs a C^*-action and a vector field which is equivariant with respect to this C^*-action. We give an explicit description of the big Bialynicky-Birula cell of the C^*-action on Mbar_00(P^n,d) as a vector bundle on Mbar_0d. This is used to calculate explicitly the cohomology ring of Mbar_00(P^n,d) in the cases d=2 and d=3. Of particular interest is the case as n approaches infinity.

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Kai Behrend, Anne O'Halloran. 2002-02-27. On the cohomology of stable map spaces. https://doi.org/10.1007/s00222-003-0308-5

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