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Walsh, Mark (2013) H-Spaces, Loop Spaces and the Space of Positive Scalar Curvature Metrics on the Sphere. Working Paper. arXiv.
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Abstract
For dimensions n greater than or equal to 3, we show that the space of metrics of positive scalar curvature on the n-sphere is homotopy equivalent to a subspace which takes the form of a H-space with a homotopy commutative, homotopy associative product operation. This product operation is based on the connected sum construction. We then exhibit an action of the little n-disks operad on this subspace which, using results of Boardman, Vogt and May implies that when n=3 or n is at least 5, the space of metrics of positive scalar curvature on the n-sphere is weakly homotopy equivalent to an n-fold loop space.
| Item Type: | Monograph (Working Paper) |
|---|---|
| Additional Information: | This is the preprint version of an article published in Geometry and Topology, 18 (2014), no. 4, 2189-2243. doi:10.2140/gt.2014.18.2189. https://projecteuclid.org/euclid.gt/1513732861 |
| Keywords: | positive scalar curvature; iterated loop space; H–space; connected sum; operad; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 10103 |
| Depositing User: | Mark Walsh |
| Date Deposited: | 16 Oct 2018 13:24 |
| Publisher: | arXiv |
| Refereed: | Yes |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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