Monoids of moduli spaces of manifolds
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
We study categories of d–dimensional cobordisms from the perspective of Tillmann [Invent. Math. 130 (1997) 257–275] and Galatius, Madsen, Tillman and Weiss [Acta Math. 202 (2009) 195–239]. There is a category C¿ of closed smooth
(d - 1)–manifolds and smooth d–dimensional cobordisms, equipped with generalised orientations specified by a map
¿: X ¿ BO(d). The main result of [Acta Math. 202 (2009) 195–239] is a determination of the homotopy type of the classifying space BC¿. The goal of the present paper is a systematic investigation of subcategories
D¿C¿ with the property that BD¿ BC¿, the smaller such D the better.
We prove that in most cases of interest, D can be chosen to be a homotopy commutative monoid. As a consequence we prove that the stable cohomology of many moduli spaces of surfaces with ¿–structure is the cohomology of the infinite loop space of a certain Thom spectrum MT¿. This was known for certain special ¿, using homological stability results; our work is independent of such results and covers many more cases.
(d - 1)–manifolds and smooth d–dimensional cobordisms, equipped with generalised orientations specified by a map
¿: X ¿ BO(d). The main result of [Acta Math. 202 (2009) 195–239] is a determination of the homotopy type of the classifying space BC¿. The goal of the present paper is a systematic investigation of subcategories
D¿C¿ with the property that BD¿ BC¿, the smaller such D the better.
We prove that in most cases of interest, D can be chosen to be a homotopy commutative monoid. As a consequence we prove that the stable cohomology of many moduli spaces of surfaces with ¿–structure is the cohomology of the infinite loop space of a certain Thom spectrum MT¿. This was known for certain special ¿, using homological stability results; our work is independent of such results and covers many more cases.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Geometry & Topology |
Vol/bind | 14 |
Sider (fra-til) | 1243-1302 |
ISSN | 1465-3060 |
DOI | |
Status | Udgivet - 2010 |
Eksternt udgivet | Ja |
Bibliografisk note
Paper id:: 10.2140/gt.2010.14.1243
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Forskningsområder
ID: 22502949