Alternative to Morse-Novikov theory for a closed 1-form. I

DOI10.1007/s40879-019-00368-xzbMath1467.55005arXiv2009.05858OpenAlexW2972765566WikidataQ127278927 ScholiaQ127278927MaRDI QIDQ2210171

Dan Burghelea

Publication date: 5 November 2020

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.05858

zbMATH Keywords

Morse-Novikov theoryNovikov-Betti numbersclosed one formconfigurations of points on the real line

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Differential forms in global analysis (58A10) Other homology theories in algebraic topology (55N35) Algebraic topology on manifolds and differential topology (57R19)

Cites Work

• Persistent homology and Floer-Novikov theory
• Topology of angle valued maps, bar codes and Jordan blocks
• A refinement of Betti numbers and homology in the presence of a continuous function, II: The case of an angle-valued map
• Topological persistence for circle-valued maps
• A refinement of Betti numbers and homology in the presence of a continuous function. I
• New Topological Invariants for Real- and Angle-Valued Maps
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