String topology for loop stacks

Kai Behrend; Grégory Ginot; Behrang Noohi; Ping Xu

doi:10.1016/j.crma.2006.10.006

String topology for loop stacks

Kai Behrend
, Grégory Ginot
, Behrang Noohi
, Ping Xu

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove that the homology groups of the free loop stack of an oriented stack are equipped with a canonical loop product and coproduct, which makes it into a Frobenius algebra. Moreover, the shifted homology H_• (L X) = H_{• + d} (L X) admits a BV algebra structure. To cite this article: K. Behrend et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

Original language	English (US)
Pages (from-to)	247-252
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	344
Issue number	4
DOIs	https://doi.org/10.1016/j.crma.2006.10.006
State	Published - Feb 15 2007

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2006.10.006

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@article{d49040ed88aa4e91bd2ae7640845711a,

title = "String topology for loop stacks",

abstract = "We prove that the homology groups of the free loop stack of an oriented stack are equipped with a canonical loop product and coproduct, which makes it into a Frobenius algebra. Moreover, the shifted homology H• (L X) = H• + d (L X) admits a BV algebra structure. To cite this article: K. Behrend et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).",

author = "Kai Behrend and Gr{\'e}gory Ginot and Behrang Noohi and Ping Xu",

note = "Funding Information: E-mail addresses: [email protected] (K. Behrend), [email protected] (G. Ginot), [email protected] (B. Noohi), [email protected] (P. Xu). 1 Research partially supported by NSF grants DMS-0306665 and DMS-0605725 \& NSA grant H98230-06-1-0047.",

year = "2007",

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doi = "10.1016/j.crma.2006.10.006",

language = "English (US)",

volume = "344",

pages = "247--252",

journal = "Comptes Rendus Mathematique",

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TY - JOUR

T1 - String topology for loop stacks

AU - Behrend, Kai

AU - Ginot, Grégory

AU - Noohi, Behrang

AU - Xu, Ping

N1 - Funding Information: E-mail addresses: [email protected] (K. Behrend), [email protected] (G. Ginot), [email protected] (B. Noohi), [email protected] (P. Xu). 1 Research partially supported by NSF grants DMS-0306665 and DMS-0605725 & NSA grant H98230-06-1-0047.

PY - 2007/2/15

Y1 - 2007/2/15

N2 - We prove that the homology groups of the free loop stack of an oriented stack are equipped with a canonical loop product and coproduct, which makes it into a Frobenius algebra. Moreover, the shifted homology H• (L X) = H• + d (L X) admits a BV algebra structure. To cite this article: K. Behrend et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

AB - We prove that the homology groups of the free loop stack of an oriented stack are equipped with a canonical loop product and coproduct, which makes it into a Frobenius algebra. Moreover, the shifted homology H• (L X) = H• + d (L X) admits a BV algebra structure. To cite this article: K. Behrend et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

UR - https://www.scopus.com/pages/publications/33846814975

UR - https://www.scopus.com/pages/publications/33846814975#tab=citedBy

U2 - 10.1016/j.crma.2006.10.006

DO - 10.1016/j.crma.2006.10.006

M3 - Article

AN - SCOPUS:33846814975

SN - 1631-073X

VL - 344

SP - 247

EP - 252

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 4

ER -

String topology for loop stacks

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