Compact and finite-type support in the homology of big mapping class groups
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Abstract For any infinite-type surface S, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface or (ii) a finite-type subsurface. Our purpose here is to study this question, in particular giving an almost-complete answer when the genus of S is positive (including infinite) and a partial answer when the genus of S is zero. Our methods involve the notion of shiftable subsurfaces as well as homological stability for mapping class groups of finite-type surfaces. |