scholarly journals The 𝑝-adic Hodge decomposition according to Beilinson

2018 ◽  
pp. 495-572 ◽  
Author(s):  
Tamás Szamuely ◽  
Gergely Zábrádi
Keyword(s):  
Hodge Decomposition

scholarly journals Hodge decomposition of string topology

2021 ◽  
Vol 9 ◽  
Author(s):  
Yuri Berest ◽  
Ajay C. Ramadoss ◽  
Yining Zhang
Keyword(s):  
Lie Algebras ◽  
General Theorem ◽  
Hodge Decomposition ◽  
String Topology ◽  
Free Loop Space ◽  
Oriented Manifold ◽  
Universal Enveloping Algebras ◽  
Finite Dimensional ◽  
Equivariant Homology ◽  
Simply Connected

Abstract Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$ -equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free loop space of X preserves the Hodge decomposition of $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ , 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].

scholarly journals On Gromov's theorem andL 2-Hodge decomposition

2004 ◽  
Vol 2004 (1) ◽  
pp. 25-44 ◽  
Author(s):  
Fu-Zhou Gong ◽  
Feng-Yu Wang
Keyword(s):  
Essential Spectrum ◽  
Vector Bundles ◽  
Functional Inequality ◽  
Upper Bounds ◽  
Hodge Decomposition ◽  
Laplace Type

Using a functional inequality, the essential spectrum and eigenvalues are estimated for Laplace-type operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the correspondingL 2-harmonic sections. In particular, some known results concerning Gromov's theorem and theL 2-Hodge decomposition are considerably improved.

scholarly journals Abstract Hodge Decomposition and Minimal Models for Cyclic Algebras

2009 ◽  
Vol 89 (1) ◽  
pp. 33-49 ◽  
Author(s):  
Joseph Chuang ◽  
Andrey Lazarev
Keyword(s):  
Hodge Decomposition ◽  
Minimal Models ◽  
Cyclic Algebras

scholarly journals Hodge decomposition and the Shapley value of a cooperative game

2019 ◽  
Vol 113 ◽  
pp. 186-198
Author(s):  
Ari Stern ◽  
Alexander Tettenhorst
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
Hodge Decomposition ◽  
The Shapley Value
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