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SUMMARY:Cohomological dimension and engulfing - Will Cavendish\, Oxford
DTSTART:20121017T150000Z
DTEND:20121017T160000Z
UID:TALK39879@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:Given a group G and a subgroup H of G\, H is said to be\nengul
 fed in G if there exists a homomorphism f from G to a\nfinite group such t
 hat f(H) is properly contained in f(G).\nThe statement that H is engulfed 
 in G can therefore be thought of\nas saying that H "looks smaller" than G 
 from the perspective of\nmaps to finite groups.  In this talk we will disc
 uss the following\nquestion: if H looks smaller than G from the perspectiv
 e of\ncohomological dimension\,  is H necessarily engulfed? While there ar
 e\nmany well-known examples that show that the answer to this question is\
 nno in general\, we will show that engulfing is guaranteed when the\ncohom
 ology rings of objects called mapping solenoids associated to the\npair (G
 \,H) satisfy certain finiteness conditions.
LOCATION:MR13
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