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2002•International Journal of MathematicsRequires access

COMBINATORIAL NOVIKOV–MORSE THEORY

Robin Forman

Open publisher page 27 citations

Abstract

In [7, 8, 9], we developed a combinatorial Morse theory which can be applied to any CW complex. In [25, 26] Novikov presented a generalization of classical Morse theory in which the Morse function is replaced by a closed 1-forms. In this paper we extend our combinatorial Morse theory to include a combinatorial analog of Novikov's theory. Along the way we introduce the notion of a combinatorial differential form which is well-suited to our work, and which may have other applications.

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What this paper is about

In [7, 8, 9], we developed a combinatorial Morse theory which can be applied to any CW complex. In [25, 26] Novikov presented a generalization of classical Morse theory in which the Morse function is replaced by a closed 1-forms. In this paper we extend our combinatorial Morse theory to include a combinatorial analog of Novikov's theory. Along the way we introduce the notion of a combinatorial differential form which is well-suited to our work, and which may have other applications.

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OpenAlex reports 27 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In [7, 8, 9], we developed a combinatorial Morse theory which can be applied to any CW complex. In [25, 26] Novikov presented a generalization of classical Morse theory in which the Morse function is replaced by a closed 1-forms. In this paper we extend our combinatorial Morse theory to include a combinatorial analog of Novikov's theory. Along the way we introduce the notion of a combinatorial differential form which is well-suited to our work, and which may have other applications.

Key concepts: Novikov self-consistency principle, Morse theory, Circle-valued Morse theory, Morse code, Discrete Morse theory, Mathematics, Generalization, Pure mathematics

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