Homotopy invariance of cohomology and signature of a Riemannian foliation

  • Georges Habib
  • Ken RichardsonEmail author


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.


Riemannian foliation Transverse geometry Basic cohomology Twisted differential Basic signature 

Mathematics Subject Classification

53C12 53C21 58J50 58J60 


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Copyright information

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Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences IILebanese UniversityFanar-MatnLebanon
  2. 2.Department of MathematicsTexas Christian UniversityFort WorthUSA

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