Stability for closed surfaces in a background space
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Stability for closed surfaces in a background space. / Cohen, Ralph L. Cohen ; Madsen, Ib Henning.
I: Homology, Homotopy and Applications, Bind 13, Nr. 2, 2011, s. 301-313.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Stability for closed surfaces in a background space
AU - Cohen, Ralph L. Cohen
AU - Madsen, Ib Henning
PY - 2011
Y1 - 2011
N2 - In this paper we present a new proof of the homological stability of the moduli space of closed surfaces in a simply connected background space K , which we denote by S g (K) . The homology stability of surfaces in K with an arbitrary number of boundary components, S g,n (K) , was studied by the authors in a previous paper. The study there relied on stability results for the homology of mapping class groups, Γ g,n with certain families of twisted coefficients. It turns out that these mapping class groups only have homological stability when n , the number of boundary components, is positive, or in the closed case when the coefficient modules are trivial. Because of this we present a new proof of the rational homological stability for S g (K) , that is homotopy theoretic in nature. We also take the opportunity to prove a new stability theorem for closed surfaces in K that have marked points.
AB - In this paper we present a new proof of the homological stability of the moduli space of closed surfaces in a simply connected background space K , which we denote by S g (K) . The homology stability of surfaces in K with an arbitrary number of boundary components, S g,n (K) , was studied by the authors in a previous paper. The study there relied on stability results for the homology of mapping class groups, Γ g,n with certain families of twisted coefficients. It turns out that these mapping class groups only have homological stability when n , the number of boundary components, is positive, or in the closed case when the coefficient modules are trivial. Because of this we present a new proof of the rational homological stability for S g (K) , that is homotopy theoretic in nature. We also take the opportunity to prove a new stability theorem for closed surfaces in K that have marked points.
M3 - Journal article
VL - 13
SP - 301
EP - 313
JO - Homology, Homotopy and Applications
JF - Homology, Homotopy and Applications
SN - 1532-0073
IS - 2
ER -
ID: 117370703