COMBINATORIAL NOVIKOV–MORSE THEORY

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.