The moduli space of generalized Morse functions

TL;DR

This paper investigates the structure and homotopy type of the space of all generalized Morse functions on d-dimensional manifolds, linking it to Morse function moduli and cobordism categories.

Contribution

It determines the homotopy type of the moduli space of generalized Morse functions, extending previous work on Morse functions and their relation to cobordism categories.

Findings

Identifies the homotopy type of the moduli space of generalized Morse functions.

Connects the moduli space to the classifying space of cobordism categories.

Provides a framework for understanding the topology of function spaces on manifolds.

Abstract

We study the moduli and determine a homotopy type of the space of all generalized Morse functions on d-manifolds for given d. This moduli space is closely connected to the moduli space of all Morse functions studied in the paper math.AT/0212321, and the classifying space of the corresponding cobordism category.