The Geometry of Loop Spaces II: Characteristic Classes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2014
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| Soggetti: | |
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| _version_ | 1866917956285366272 |
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| author | Maeda, Yoshiaki Rosenberg, Steven Torres-Ardila, Fabián |
| author_facet | Maeda, Yoshiaki Rosenberg, Steven Torres-Ardila, Fabián |
| contents | Using the Wodzicki residue, we build Wodzicki-Chern-Simons (WCS) classes in $H^{2k-1}(LM)$ associated to the residue Chern character on the loop space $LM$ of a Riemannian manifold $M^{2k-1}$. These WCS classes are associated to the $L^2$ connection and the Sobolev $s=1$ connections on $LM.$ The WCS classes detect several families of 5-manifolds whose isometry group has infinite fundamental group. These manifolds are the total spaces of the circle bundles associated to a multiple $pω, |p|\gg 0$, of the Kähler form $ω$ over an integral Kähler surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1407_2491 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | The Geometry of Loop Spaces II: Characteristic Classes Maeda, Yoshiaki Rosenberg, Steven Torres-Ardila, Fabián Differential Geometry Using the Wodzicki residue, we build Wodzicki-Chern-Simons (WCS) classes in $H^{2k-1}(LM)$ associated to the residue Chern character on the loop space $LM$ of a Riemannian manifold $M^{2k-1}$. These WCS classes are associated to the $L^2$ connection and the Sobolev $s=1$ connections on $LM.$ The WCS classes detect several families of 5-manifolds whose isometry group has infinite fundamental group. These manifolds are the total spaces of the circle bundles associated to a multiple $pω, |p|\gg 0$, of the Kähler form $ω$ over an integral Kähler surface. |
| title | The Geometry of Loop Spaces II: Characteristic Classes |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1407.2491 |