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An analytic Novikov conjecture for semigroups. (English) Zbl 1403.19006

The author formulates an analytic assembly map for semigroups and conjectures that the map is injective for torsion-free semigroups, which is an analytic Novikov conjecture for semigroups. The author also shows that the decent argument from the coarse Baum-Connes conjecture works in the same way as it does for groups. In order to carry it out, the author generalizes parts of equivariant homology theory for group actions to the semigroup case. The paper also includes some examples where the decent argument works.

MSC:

19K56 Index theory
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References:

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