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SUMMARY:Topology of ends of nonpositively curved manifolds - Grigori Avram
 idi (Universität Münster)
DTSTART:20170623T123000Z
DTEND:20170623T133000Z
UID:TALK73046@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-author: Tam Nguyen Phan		(Binghamton University)     
    <br></span><span><br>The structure of ends of a finite volume\, nonposi
 tively curved\, locally symmetric manifold M is very well understood. By B
 orel-Serre\, the thin part of the universal cover of such a manifold is ho
 motopy equivalent to a rational Tits building. This is a simplicial comple
 x built out of the algebra of the locally symmetric space which turns out 
 to have dimension <M/2. In this talk\, I will explain aspects of the local
 ly symmetric situation that are true for more general finite volume nonpos
 itively curved manifolds satisfying a mild tameness assumption (there are 
 no arbitrarily small closed geodesic loops). The main result is that the h
 omology of the thin part of the universal cover vanishes in dimension grea
 ter or equal to dim M/2. One application is that any complex X homotopy eq
 iuvalent to M has dimension >= dim M/2. Another application is that the gr
 oup cohomology with group ring coefficients of the fundamental group of M 
 vanishes in low dimensions (<dim M/2).&nbsp\;</span>
LOCATION:Seminar Room 1\, Newton Institute
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