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arXiv · 0912.2505

Embedded Cobordism Categories and Spaces of Manifolds

Oscar Randal-Williams
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Abstract

Galatius, Madsen, Tillmann and Weiss have identified the homotopy type of the classifying space of the cobordism category with objects (d-1)-dimensional manifolds embedded in R^\infty. In this paper we apply the techniques of spaces of manifolds, as developed by the author and Galatius, 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 Poincare duality, relating a space of submanifolds of M to a space of functions on M.

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BibTeXRIS

Oscar Randal-Williams. 2009-12-13. Embedded Cobordism Categories and Spaces of Manifolds. https://doi.org/10.1093/imrn%2Frnq072

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