Embedded Cobordism Categories and Spaces of Submanifolds
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Embedded Cobordism Categories and Spaces of Submanifolds. / Randal-Williams, Oscar.
In: International Mathematics Research Notices, Vol. 2011, No. 3, 2011, p. 572-608.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Embedded Cobordism Categories and Spaces of Submanifolds
AU - Randal-Williams, Oscar
PY - 2011
Y1 - 2011
N2 - Galatius, Madsen, Tillmann, and Weiss [7] have identified the homotopy type of the classifying space of the cobordism category with objects (d -1)-dimensional manifolds embedded in R8. In this paper we apply the techniques of spaces of manifolds, as developed by the author and Galatius in [8], to identify the homotopy type of the cobordism category with objects (d -1)-dimensional submanifolds of a fixed background manifold M. There is a description in terms of a space of sections of a bundle over M associated to its tangent bundle. This can be interpreted as a form of Poincaré duality, relating a space of submanifolds of M to a space of functions on M.
AB - Galatius, Madsen, Tillmann, and Weiss [7] have identified the homotopy type of the classifying space of the cobordism category with objects (d -1)-dimensional manifolds embedded in R8. In this paper we apply the techniques of spaces of manifolds, as developed by the author and Galatius in [8], to identify the homotopy type of the cobordism category with objects (d -1)-dimensional submanifolds of a fixed background manifold M. There is a description in terms of a space of sections of a bundle over M associated to its tangent bundle. This can be interpreted as a form of Poincaré duality, relating a space of submanifolds of M to a space of functions on M.
U2 - 10.1093/imrn/rnq072
DO - 10.1093/imrn/rnq072
M3 - Journal article
VL - 2011
SP - 572
EP - 608
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 3
ER -
ID: 22502971