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September 6, 2014

Ronnie Brown in Paris

Posted by David Corfield

Ronnie Brown has brought to my attention a talk he gave recently at the Workshop Constructive Mathematics and Models of Type Theory, IHP Paris, 02 June 2014 - 06 June 2014.

Title: Intuitions for cubical methods in nonabelian algebraic topology

Abstract: The talk will start from the 1-dimensional Seifert-van Kampen Theorem for the fundamental group, then groupoid, and so to a use of strict double groupoids for higher versions. These allow for some precise nonabelian calculations of some homotopy types, obtained by a gluing process. Cubical methods are involved because of the ease of writing multiple compositions, leading to “algebraic inverses to subdivision”, relevant to higher dimensional local-to-global problems. Also the proofs involve some ideas of 2-dimensional formulae and rewriting. The use of strict multiple groupoids is essential to obtain precise descriptions as colimits and hence precise calculations. Another idea is to use both a “broad” and a “narrow” model of a particular kind of homotopy types, where the broad model is used for conjectures and proofs, while the narrow model is used for calculations and relation to classical methods. The algebraic proof of the equivalence of the two models then gives a powerful tool.

Slides are available from his preprint page.

Posted at September 6, 2014 10:47 AM UTC

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