Notes on factorization algebras, factorization homology and applications

By Grégory Ginot. 2013

67 citations recorded by the source corpus.

These notes are an expanded version of two series of lectures given at the winter school in mathematical physics at les Houches and at the Vietnamese Institute for Mathematical Sciences. They are an introduction to factorization algebras, factorization homology and some of their applications, notably for studying $E_n$-algebras. We give an account of homology theory for manifolds (and spaces), which give invariant of manifolds but also invariant of $E_n$-algebras. We particularly emphasize the point of view of factorization algebras (a structure originating from quantum field theory) which plays, with respect to homology theory for manifolds, the role of sheaves with respect to singular cohomology. We mention some applications to the study of mapping spaces and study several examples, including some over stratified spaces.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f1184f8d4cc071bd94a19ecb9e7bc28379711573

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In Algebra and Number Theory

1. David Ben-Zvi
2. D. Jordan
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4. S. Witherspoon
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In Geometry and Topology

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Citations in the corpus

• Quantum character varieties and braided module categories (2016, background): “[2,35]) that the structure of Enmodule over an En-algebraA onM is equivalent to the structure of left module over the associative (E1) “universal enveloping algebra” U (A), namely the factorization homology U (A) = ∫Ann A of an annulus with coefficients in A.”