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Universität Augsburg
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Universität Augsburg
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Herr Arber Selimi
Universität Bonn
spricht am
Dienstag, 4. September 2018
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| For the n-th Braid group $B_n$, and a given discrete group G the Hurwitz space is defined as the Borel construction $$\textrm{Hur}_{G,n}=EB_n\times _{B_n} G^n.$$ where the action of $B_n$ on $G^n$ is given by $$\sigma_i (g_1,...,g_i,g_{i+1},...,g_n)=(g_1,...,g_ig_{i+1}g_i^{-1},g_{i},...,g_n).$$ Since a single conjugacy class (or union of conjugacy classes ) c of G is invariant under $B_n$ action, we can consider $$\textrm{Hur}^c_{G,n}=EB_n\times _{B_n} c^n.$$ The fact that $$\sqcup_{n\geq 0} \textrm{Hur}^c_{G,n}$$ is an associative H space induces a ring structure on $$R=\bigoplus_{n\geq 0} H_0 (\textrm{Hur}^c_{G,n})$$ and an R-module structure on $$M_p= \bigoplus_{n\geq 0} H_p (\textrm{Hur}^c_{G,n}),$$ for all p. If the ring of coefficients is a field $k$ and $G$ a finite group such that the order of $G$ is invertible on $k$ and the pair $(G,c)$ satisfies the non-splitting property (or c invariably generates G) then a Homologcal stability for zeroth Homology holds. Using this result and a spectral sequence converging to the Homology of Hurwitz spaces a stability theorem for higer homologies can be shown. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Bernhard Hanke |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).