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Hodge Theory and String Topology.

Xiong, Xin.

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Hodge Theory and String Topology.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Hodge Theory and String Topology./
Author:	Xiong, Xin.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	69 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
Contained By:	Dissertations Abstracts International82-12B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28321831
ISBN:	9798738637674

Hodge Theory and String Topology.
Xiong, Xin.

Hodge Theory and String Topology. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 69 p.

Source: Dissertations Abstracts International, Volume: 82-12, Section: B.

Thesis (Ph.D.)--Duke University, 2021.

This item must not be sold to any third party vendors.

Let M be an oriented smooth manifold of dimension n. The free loop space λM of M is the space of piecewise smooth maps from the circle to M. Chas and Sullivan defined the string productCS : Hi (λM; ℤ) ⊗ Hj (λM; ℤ) → ︱H i+j-n (λM; ℤ).Goresky and Hingston defined a string coproductGH : Hk (λM,M;ℚ) → ⊕ i+j=k-n+1 Hi(λM,M;ℚ) ⊗ Hj(λM,M;ℚ) .When M is a simply-connected complex algebraic manifold, the cohomology of λM has a natural mixed Hodge structure with weights greater or equal to cohomological degree. In this case, we show that the string operations, CS and GH, are morphisms of mixed Hodge structure after a suitable Tate twist. We prove this by giving a de Rham description of the string operations in terms of Chen's iterated integrals.

ISBN: 9798738637674Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Manifold dimensions

Hodge Theory and String Topology.
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020 $a 9798738637674
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100 1 $a Xiong, Xin. $3 2105938
245 1 0 $a Hodge Theory and String Topology.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 69 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
500 $a Advisor: Hain, Richard.
502 $a Thesis (Ph.D.)--Duke University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Let M be an oriented smooth manifold of dimension n. The free loop space λM of M is the space of piecewise smooth maps from the circle to M. Chas and Sullivan defined the string productCS : Hi (λM; ℤ) ⊗ Hj (λM; ℤ) → ︱H i+j-n (λM; ℤ).Goresky and Hingston defined a string coproductGH : Hk (λM,M;ℚ) → ⊕ i+j=k-n+1 Hi(λM,M;ℚ) ⊗ Hj(λM,M;ℚ) .When M is a simply-connected complex algebraic manifold, the cohomology of λM has a natural mixed Hodge structure with weights greater or equal to cohomological degree. In this case, we show that the string operations, CS and GH, are morphisms of mixed Hodge structure after a suitable Tate twist. We prove this by giving a de Rham description of the string operations in terms of Chen's iterated integrals.
590 $a School code: 0066.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Manifold dimensions
653 $a Free loop space
653 $a Piecewise smooth maps
653 $a String products and coproducts
653 $a Complex algebraic manifold
653 $a Cohomology
653 $a Mixed Hodge structure
653 $a String operations
653 $a Morphisms
690 $a 0405
690 $a 0642
710 2 $a Duke University. $b Mathematics. $3 1036449
773 0 $t Dissertations Abstracts International $g 82-12B.
790 $a 0066
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28321831