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Homotopy invariance of cohomology and signature of a Riemannian foliation
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 ba...
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Published in: | Mathematische Zeitschrift 2019-10, Vol.293 (1-2), p.579-595 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | 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 Álvarez class of a Riemannian foliation is invariant under foliated homotopy equivalence. |
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ISSN: | 0025-5874 1432-1823 |
DOI: | 10.1007/s00209-018-2195-x |