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Homotopy theory, homological algebra, algebraic treatments of manifolds.

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Does the Deligne-Mumford space module $S_{n}$ action have a fundamental chain?

Does the Deligne-Mumford space (without ordering for marked points) $\bar M_{g,n}/S_{n}$ has fundamental chain in signular simplicial chains? (because I read Costello's paper GW potential to TCFT, as …
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