(Homotopy) algebras and (pointed) bimodules over them can be viewed as factorization algebras on the real line $\mathbb{R}$ which are locally constant with respect to a certain stratification. Moreover, Lurie proved that $E_n$-algebras are equivalent to locally constant factorization algebras on $\mathbb{R}^n$. Starting from these two facts I will explain how to model the Morita category of $E_n$-algebras as an $(\infty, n)$-category. Every object in this category, i.e. any $E_n$-algebra $A$, is "fully dualizable" and thus gives rise to a fully extended TFT by the cobordism hypothesis of Baez-Dolan-Lurie. I will explain how this TFT can be explicitly constructed by (essentially) taking factorization homology with coefficients in the $E_n$-algebra $A$.

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Speaker:

Claudia Scheimbauer
Affiliation:

MPIM
Date:

Wed, 2015-01-28 10:30 - 12:00
Location:

MPIM Lecture Hall
Parent event:

Higher Differential Geometry Seminar