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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1703.10448 |
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| _version_ | 1866917693638049792 |
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| author | Habib, Georges Richardson, Ken |
| author_facet | Habib, Georges Richardson, Ken |
| contents | We prove that any smooth foliation that admits a Riemannian foliation structure has a well-defined basic signature, and this geometrically defined invariant is actually a foliated homotopy invariant. We also show that foliated homotopic maps between Riemannian foliations induce isomorphic maps on basic Lichnerowicz cohomology, and that the Alvarez class of a Riemannian foliation is invariant under foliated homotopy equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_10448 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Homotopy invariance of cohomology and signature of a riemannian foliation Habib, Georges Richardson, Ken Differential Geometry We prove that any smooth foliation that admits a Riemannian foliation structure has a well-defined basic signature, and this geometrically defined invariant is actually a foliated homotopy invariant. We also show that foliated homotopic maps between Riemannian foliations induce isomorphic maps on basic Lichnerowicz cohomology, and that the Alvarez class of a Riemannian foliation is invariant under foliated homotopy equivalence. |
| title | Homotopy invariance of cohomology and signature of a riemannian foliation |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1703.10448 |