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A Batalin-Vilkovisky algebra morphism from double loop spaces to free loops | Luc Menichi
; | Date: |
13 Aug 2009 | Abstract: | Let $M$ be a compact oriented $d$-dimensional smooth manifold and $X$ a
topological space. Chas and Sullivan cite{Chas-Sullivan:stringtop} have
defined a structure of Batalin-Vilkovisky algebra on
$mathbb{H}_*(LM):=H_{*+d}(LM)$. Getzler cite{Getzler:BVAlg} has defined a
structure of Batalin-Vilkovisky algebra on the homology of the pointed double
loop space of $X$, $H_*(Omega^2 X)$. Let $G$ be a topological monoid with a
homotopy inverse. We define a structure of Batalin-Vilkovisky algebra on
$H_*(Omega^2BG)otimesmathbb{H}_*(M)$ extending the Batalin-Vilkovisky
algebra of Getzler on $H_*(Omega^2BG)$. We prove that the morphism of graded
algebras $$H_*(Omega^2BG)otimesmathbb{H}_*(M) omathbb{H}_*(LM)$$ defined
by Felix and Thomas cite{Felix-Thomas:monsefls}, is in fact a morphism of
Batalin-Vilkovisky algebras. In particular, if $G=M$ is a connected Lie group,
$H_*(Omega^2 BG)$ is a trivial sub Batalin-Vilkovisky algebra of
$mathbb{H}_*(LG)$. | Source: | arXiv, 0908.1883 | Services: | Forum | Review | PDF | Favorites |
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