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

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
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
Publication status	Published - 15 Feb 2007
Externally published	Yes

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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).",

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AU - Behrend, Kai

AU - Ginot, Grégory

AU - Noohi, Behrang

AU - Xu, Ping

PY - 2007/2/15

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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).

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DO - 10.1016/j.crma.2006.10.006

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SN - 1631-073X

VL - 344

SP - 247

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 4

ER -

String topology for loop stacks

Abstract

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