Delocalized Betti numbers and Morse type inequalities
Mostafa Esfahani Zadeh
TL;DR
This paper establishes Morse type inequalities involving delocalized Betti numbers for Morse functions and closed 1-forms, leading to results on the vanishing of these Betti numbers for certain fibered manifolds.
Contribution
It introduces Morse inequalities for delocalized Betti numbers and applies them to prove their vanishing in specific fibering cases.
Findings
Morse inequalities for delocalized Betti numbers
Vanishing of delocalized Betti numbers for manifolds fibering over the circle
Extension of Morse theory to delocalized invariants
Abstract
In this paper we state and prove Morse type inequalities for Morse functions as well as for closed differential 1-forms. These inequalities involve delocalized Betti numbers. As an immediate consequence, we prove the vanishing of delocalized Betti numbers of manifolds fibering over the circle.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Mathematical functions and polynomials · Advanced Mathematical Theories and Applications