Topology of spaces of S-immersions

TL;DR

This paper characterizes the homotopy type of the space of S-immersions, which are equidimensional folded maps with prescribed folds, using the wrinkling theorem to provide a comprehensive topological description.

Contribution

It applies the wrinkling theorem to fully describe the homotopy type of the space of S-immersions, advancing understanding of their topology.

Findings

Homotopy type of S-immersions space characterized

Application of wrinkling theorem to equidimensional maps

Provides a complete topological description

Abstract

We use the wrinkling theorem proven in Y. Eliashberg and N. Mishachev, "Wrinkling of smooth mappings and its applications - I", Invent. Math., 130(1997), 345-369, to fully describe the homotopy type of the space of S-immersions, i.e. equidimensional folded maps with prescribed folds.