A generalized Blakers-Massey Theorem

12 Oct 2016, 15:20
50m
Amphi Lavoisier ()

Amphi Lavoisier

Contributed talk Topologie algébrique et applications

Speaker

Dr Georg Biedermann (LAGA, Paris 13)

Description

(joint with M. Anel, E. Finster, and A. Joyal) We present a generalized version of the Blakers-Massey Theorem in the context of $\infty$-topoi. The proof refines a proof of the classical theorem by Finster and Lumsdaine given in the language of Homotopy Type Theory and its "re-engineered" version by Rezk. The main tools are certain factorization systems (modality) and homotopical descent. The classical theorem and a recent generalization due to Chacholski-Scherer-Werndli are easy consequences. As an application we prove a conjecture by Goodwillie: a Blakers-Massey Theorem for the calculus of homotopy functors. From it we obtain an independent proof of the fact that homogeneous functors deloop.

Primary author

Dr Georg Biedermann (LAGA, Paris 13)

Presentation Materials