Hodge decomposition of string topology
Y Berest, AC Ramadoss, Y Zhang - Forum of Mathematics, Sigma, 2021 - cambridge.org
Y Berest, AC Ramadoss, Y Zhang
Forum of Mathematics, Sigma, 2021•cambridge.orgLet X be a simply connected closed oriented manifold of rationally elliptic homotopy type.
We prove that the string topology bracket on the-equivariant homology of the free loop space
of X preserves the Hodge decomposition of, making it a bigraded Lie algebra. We deduce
this result from a general theorem on derived Poisson structures on the universal enveloping
algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles
a conjecture of [7].
We prove that the string topology bracket on the-equivariant homology of the free loop space
of X preserves the Hodge decomposition of, making it a bigraded Lie algebra. We deduce
this result from a general theorem on derived Poisson structures on the universal enveloping
algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles
a conjecture of [7].
Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the -equivariant homology of the free loop space of X preserves the Hodge decomposition of , making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles a conjecture of [7].
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