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Barcelona Algebraic Topology Group
Barcelona Topology Workshop 2016. Spring Session PDF Print E-mail
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Monday, 06 June 2016 14:50

The Barcelona Topology Workshop is the annual meeting of the Grup de Topologia Algebraica de Barcelona. 
The Spring Session of the Barcelona Topology Workshop 2016 will take place on the 10-11th June, 2016, at the CRM in Barcelona (on the UAB campus).



This is the web site of the Algebraic Topology Team in Barcelona (Grup de Topologia Algebraica de Barcelona, 2014SGR-42 and Homotopy theory of classifying spaces and function complexes, MTM2013-42293-P).

Our research interests include a variety of subjects in algebraic topology, group theory, homological algebra, and category theory. Here you will find information about us and our common activities.

Friday's Topology Seminar 2015-2016 PDF

This semester we will read Benson-Greenlees paper "Stratifying the derived category of cochains on $BG$ for $G$ a compact Lie group".

Our aim will be study the results and see if we can generalize them to the $p$-compact case. The tentative schedule is the following:

1) February 19th. W. Pitsch. Overview
2) March 4th. L. Carlier. Tensor triangualted categories
3) April 1st. T. Lozano. $p$-compact groups
4) April 15th. W. Pitsch. Stratification I
5) April 29th. W. Pitsch Stratification II
6) May 6th. J. Kock Pointfree Topology on Spec R and support I
7) May 13rd. J. Kock Pointfree Topology on Spec R and support II
8) May 20th W. Pitsch Some results on D(R) for R a ring spectrum

Date and place: Fridays 12h00-13h00, CRM Room A1.


Extraordinary session:

Date and Place: June 9th 12h00, CRM room A1
Michael Batanin (Macquarie Univeristy)
A less known Deligne's conjecture

Abstract: A now famous Deligne's conjecture on Hochschild cochains (proved
by many authors) asserts that this complex is naturally a
E_2-algebra i.e. an algebra of an operad weakly equivalent to
the little 2-disk operad.

In 1992 Alexey Davydov introduced a construction of a
deformation complex of a monoidal functor which reminds the
classical Hochschild complex but in many respect is a very
different creature.  For example, you can apply this
construction to the identity functor.  The corresponding
cohomology classify obstructions for infinitesimal deformations
of the associator of a tensor category (like classical
Hochschild cohomology classify obstructions for infinitesimal
deformations of the multiplication of an associative algebra).
So, in some sense, this is a second order or categorification of
the Hochschild cohomology.  Deligne (in a letter to Davydov in
1993) suggested a simple algebraic condition called
n-commutativity for a cosimplicial complex of associative
algebras and conjectured that an n-commutative complex has a
natural E_{n+1}-algebra structure.  It can be easily proved that
in general Davydov's complex is a 1-commutative complex in
Deligne's sense but the deformation complex of an identity
functor is 2-commutative.

Regular seminar:

Date and Place: June 3rd 12h00, CRM room A1
Natàlia Castellana (UAB)
Noetherianity in cohomology

Abstract: We will show why various cohomologies of interest (p-compact group, p-local groups) have noetherian cohomology. The proofs rest on nice properties of various transfers in these different settings.



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