Mathematics – Algebraic Topology
Scientific paper
2008-11-14
Mathematics
Algebraic Topology
82 pages. Second version with remarks on higher category approaches and various minor corrections
Scientific paper
In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex structures along with a holomorphic map to a target complex manifold. A general notion of "geometric structure" is defined using sheaf theoretic constructions. Our main theorem is the identification of the homotopy type of such cobordism categories in terms of certain Thom spectra. This extends work of Galatius-Madsen-Tillmann-Weiss who identify the homotopy type of cobordism categories of manifolds with fiberwise structures on their tangent bundles. Interpretations of the main theorem are discussed which have relevance to topological field theories, moduli spaces of geometric structures, and h-principles. Applications of the main theorem to various examples of interest in geometry, particularly holomorphic curves, are elaborated upon.
No associations
LandOfFree
Geometric Cobordism Categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Geometric Cobordism Categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric Cobordism Categories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-10856