Unimodular homotopy algebras and Chern-Simons theory

Braun, Christopher and Lazarev, Andrey (2015) Unimodular homotopy algebras and Chern-Simons theory. Journal of Pure and Applied Algebra, 219 (11). pp. 5158-5194. ISSN 0022-4049

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Abstract

Quantum Chern–Simons invariants of differentiable manifolds are analyzed from the point of view of homological algebra. Given a manifold M and a Lie (or, more generally, an L∞) algebra g, the vector space H⁎(M)⊗g has the structure of an L∞ algebra whose homotopy type is a homotopy invariant of M . We formulate necessary and sufficient conditions for this L∞ algebra to have a quantum lift. We also obtain structural results on unimodular L∞ algebras and introduce a doubling construction which links unimodular and cyclic L∞ algebras.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Pure and Applied Algebra
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2602
Subjects:
ID Code:
73671
Deposited By:
Deposited On:
18 Jun 2015 05:40
Refereed?:
Yes
Published?:
Published
Last Modified:
26 May 2020 04:00