Department Mathematik



Mathematisches Kolloquium

Am Donnerstag, 23. Juni 2016, um 16:30 Uhr spricht

Emmanuel Dror Farjoun
(Hebräische Universität Jerusalem )

im Hörsaal A027 über das Thema

A path From Discrete to Topological groups

Zusammenfassung: Question: Given a map of discrete groups f:G---->H when is this map induced from a normal subgroup inclusion of topological groups X\subseteq Y by taking path components of G and H? For example, the trivial map on the integers Z--->0 arise in this way via the inclusion $Z\subseteq R$ of the integers in the additive group of real numbers. However, the trivial map on a non commutative group G---> 1 cannot arise from such a normal inclusion of topological groups by taking the induced map on path components. In considering this question one builds from the given map f of discrete groups an associated topological space Q:= H//G= H_hG the "homotopy quotient", and attempts to put a group structure on Q. This is not possible in general, for example if Q has non abelian fundamental group. We will discuss similar constructions which are standard in topology and show that a full answer to the above question is given by a simple extra structure on the given map G-->H and lies with a well known notion of crossed module and an observation due to Quillen. ( joint work with Y. Segev.)
Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.
Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.