Transferring homotopy commutative algebraic structures
By Xuehan Cheng, E. Getzler. 2006
66 citations recorded by the source corpus.
Abstract We show that the sum over planar tree formula of Kontsevich and Soibelman transfers C ∞ -structures along a contraction. Applying this result to a cosimplicial commutative algebra A • over a field of characteristic zero, we exhibit a canonical C ∞ -structure on Tot ( A • ) , which is unital if A • is; in particular, we obtain a canonical C ∞ -structure on the cochain complex of a simplicial set.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/31617c09f2828ee7e6b6a64d0d814961a5da9286
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Homological perturbation theory for algebras over operads (2009, methodology): “ explicit tree formulas for transferring A∞-algebra structures, and remarked that their formulas should work also for algebras over more general operads. That they work for C∞-algebras was verified in [7]. Huebschmann [20] has recently given an account of how, in the A∞ case, the tree formulas can be”