Poincare Duality of Morse-Novikov Cohomology on a Riemannian Manifold

Abstract

Morse-Novikov or Lichnerowicz cohomology groups of a manifold has been studied by researchers to deduce properties and invariants of manifolds. Morse-Novikov cohomology is defined using the twisted differential d_ω = d +ω∧, where d is the usual differential operator on forms, and ω is a non-exact closed 1-form on the manifold. On a Riemanian manifold each Morse-Novikov cohomolgy class has unique harmonic representative, and has Poincare duality isomorphism. This isomorhism have been proved in many elegant ways in literature. In this article we provide yet another proof using ellepticity of a differential complex, Green’s operator, and Hodge star operator which may be useful in other computations related to Morse-Novikov cohomology.

GANITJ. Bangladesh Math. Soc.41.2 (2021) 34-40