Mini-course: Homology decompositions and applications

Thời gian: 14:30:06/10/2015 đến 16:30:26/12/2015

Địa điểm: Vietnam Institute for Advanced Study in Mathematics

Mục đích: Xem phần tóm tắt nội dung.

Tóm tắt:

1) Begin with recalls on homotopy colimits (and homotopy limits).

2) Relate the classifying space BG of a compact Lie group G with the homotopy colimit of the diagram of the centralizers of the elementary abelian p-subgroups E ⊂ G (result of S. Jackowski and J. McClure: Homotopy decomposition of classifying spaces via elementary abelian subgroups, Topology 31, 1992, 113-132); my presentation will follow the one by W. G. Dwyer and C. W. Wilkerson: A cohomology decomposition theorem, Topology 31, 1992, 433–443.

3) Explain the generalization uncovered by Hans-Werner Henn where BG is replaced with some suitable Borel construction: Centralizers of elementary abelian p-subgroups, the Borel construction of the singular locus and applications to the cohomology of discrete groups, Topology 36, 1997, 271-286.
4) Finally, use what preceeds to get information on the cohomology of some arithmetic groups (unpublished work with Hans-Werner Henn). On this occasion, the theory of lattices will be used and an incursion in the world of buildings will be made.

5) If there is enough time, there will be also lecture on higher Hopf invariants (quite a different matter). An alternative would be to run a seminar on the subject.