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SUMMARY:Hopf Formulae for TOR - Julia Goedecke (University of Cambridge)
DTSTART:20170314T141500Z
DTEND:20170314T151500Z
UID:TALK71416@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:A Hopf formula expresses a homology object in terms of a proje
 ctive\npresentation\, its kernel and certain (generalised) commutators. Th
 e\nfirst one\, for second group homology\, was given by Hopf in 1942. Over
 \nthe last 13 years or so\, Everaert\, Gran\, Van der Linden and others ha
 ve\ndeveloped Hopf formulae in more general categorical contexts. One of\n
 these general contexts is that of a semi-abelian category with a\nBirkhoff
  subcategory where the reflector factors through a protoadditive\nfunctor.
  In that generality\, some elements of the Hopf formula are\nnecessarily v
 ery abstract. With Tim Van der Linden and Guram Donadze\, I am studying th
 e special situation of subvarieties of categories of\nR-modules. Here we c
 an find explicit and easy formulations of the\ngeneralised commutators. Si
 nce the reflector in this situation turns out\nto be tensoring\, the resul
 ting homology functors are Tor functors.\nThrough these fairly simple form
 ulations we obtain new ways of\ncalculating\, for example\, homology of Li
 e algebras\, and Hochschild\nHomology of an associative unital algebra. Mo
 re generally\, we will be\nable to cover the situation of any *abelian* Bi
 rkhoff subcategory of a\nsemi-ablian category with this easier formulation
 .
LOCATION:MR5\, Centre for Mathematical Sciences
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