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Cohomological dimension and engulfing
If you have a question about this talk, please contact Ivan Smith.
Given a group G and a subgroup H of G, H is said to be engulfed in G if there exists a homomorphism f from G to a finite group such that f(H) is properly contained in f(G). The statement that H is engulfed in G can therefore be thought of as saying that H “looks smaller” than G from the perspective of maps to finite groups. In this talk we will discuss the following question: if H looks smaller than G from the perspective of cohomological dimension, is H necessarily engulfed? While there are many well-known examples that show that the answer to this question is no in general, we will show that engulfing is guaranteed when the cohomology rings of objects called mapping solenoids associated to the pair (G,H) satisfy certain finiteness conditions.
This talk is part of the Differential Geometry Seminar series.
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