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Barcelona Algebraic Topology Group

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Friday's Topology Seminar 2013-2014


Date and place: July 18, 2014. 12am. CRM, small lecture room.
Speaker : Shizuo Kaji (Yamaguchi U)
A product in equivariant homology for compact Lie group actions
The Tate cohomology for a finite group integrates group homology and cohomology into one theory. It is equipped with a cup product, which coincides with the usual one on cohomology and gives a ring structure on homology. A few attempts have been made to generalise this product structure on homology. We follow the line of Kreck and Tene. Kreck defined a product on H_*(BG;Z) for a compact Lie group G based on his geometric homology theory and Tene showed it coincides with the cup product on the Tate cohomology when G is finite. We will generalise this product to one on the equivariant homology of a manifold with a nice action of a Lie group. Our construction is simple and purely homotopy theoretical. This is a joint work with Haggai Tene.

Date and place: June 20, 2014. 12am. CRM, small lecture room.
Speaker : Conchita Martínez (U Zaragoza)
Title: On dimension invariants for groups admitting a cocompact model for proper actions.

Friday's Topology Seminar 2012-2013

Friday June 7th, 2013, CRM (Aula petita):

12:00 Dietrich Notbohm : Depth and homology decompositions

Abstract:  Homology decomposition techniques are
a powerful tool used in the analysis of the homotopy theory of (classifying)
spaces. The associated Bousfield-Kan spectral sequences involve higher
derived limits of the inverse limit functor. We study the impact of
depth conditions on the vanishing of these higher limits and apply our theory
in several cases,. In particular we will dicuss our theory in the context of group cohomology and  of polynomial invariants.

Check the calendar for upcoming events

Friday's Topology Seminar 2011-2012

July 9th, 2012, 15:30 CRM.

José Cantarero (Stanford University), "El espacio de órbitas de un grupo p-compacto".

Abstract: Para un grupo finito G, el complejo de Brown es el G-poset de cadenas de p-subgrupos no triviales ordenados por inclusión de cadenas, donde G actúa por conjugación. P. Webb conjeturó que el espacio de órbitas de esta acción es contráctil. Esta  conjetura fue demostrada por P. Symonds. Recientemente han aparecido versiones de este resultado para sistemas de fusión y grupos compactos de Lie. En esta charla se discutirá una generalización de este resultado y las técnicas de una demostración que aplica a todos estos casos y que además proporciona un nuevo resultado para grupos p-compactos y espacios de lazos finitos.

June 15th, 2012, 10:00 CRM.

Bob Oliver (Université Paris Nord), "Reduced fusion systems over 2-groups of sectional rank at most four".

Abstract: The sectional rank of a $p$-group is the largest rank of any of its abelian subquotients. One of the steps towards classifying finite simple groups was the 1974 book by Gorenstein and Harada, where they list all finite simple groups whose Sylow 2-subgroup has sectional rank at most four.
I want to describe a similar result, listing all reduced fusion systems over 2-groups of sectional rank at most four. The list contains no surprises: it consists entirely of fusion systems of simple groups on the Gorenstein-Harada list. But the method of proof seems very different, since it is based on studying the different types of essential subgroups which can occur, rather than the centralizers of involutions. This also leads to a different way of organizing the final result, which I hope will be of interest.

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