The algebraic construction of the Novikov complex of a circle-valued Morse function
Andrew Ranicki
TL;DR
This paper presents an algebraic method to construct the Novikov complex for circle-valued Morse functions, utilizing the Morse-Smale complex on a fundamental domain of the infinite cyclic cover.
Contribution
It introduces an algebraic construction of the Novikov complex based on the Morse-Smale complex, providing a new approach to analyze circle-valued Morse functions.
Findings
Algebraic construction of the Novikov complex from Morse-Smale complex
Application to circle-valued Morse functions via infinite cyclic covers
Provides a new framework for studying Morse theory on circle-valued functions
Abstract
The Novikov complex of a circle-valued Morse function is constructed algebraically from the Morse-Smale complex of the restriction to a fundamental domain of the real-valued Morse function on the pullback infinite cyclic cover.
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Taxonomy
TopicsTopological and Geometric Data Analysis · advanced mathematical theories · Mathematical Dynamics and Fractals