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Parametrised moduli spaces of surfaces as infinite loop spaces
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Journal Article
Parametrised moduli spaces of surfaces as infinite loop spaces
2022
Overview
We study the
$E_2$
-algebra
$\\Lambda \\mathfrak {M}_{*,1}:= \\coprod _{g\\geqslant 0}\\Lambda \\mathfrak {M}_{g,1}$
consisting of free loop spaces of moduli spaces of Riemann surfaces with one parametrised boundary component, and compute the homotopy type of the group completion
$\\Omega B\\Lambda \\mathfrak {M}_{*,1}$
: it is the product of
$\\Omega ^{\\infty }\\mathbf {MTSO}(2)$
with a certain free
$\\Omega ^{\\infty }$
-space depending on the family of all boundary-irreducible mapping classes in all mapping class groups
$\\Gamma _{g,n}$
with
$g\\geqslant 0$
and
$n\\geqslant 1$
.
Publisher
Cambridge University Press
Subject
