Real map germs and higher open books

TL;DR

This paper establishes criteria for the existence of open book structures in real map germs with isolated critical points or values, including weighted-homogeneous maps, expanding understanding of their topological properties.

Contribution

It provides a general criterion for open book structures in real map germs and identifies conditions satisfied by weighted-homogeneous maps.

Findings

Criteria for open book structures in real map germs.

Weighted-homogeneous maps satisfy these criteria.

Sufficient conditions for map germs with isolated critical value.

Abstract

We present a general criterion for the existence of open book structures defined by real map germs $(\bR^m, 0) \to (\bR^p, 0)$, where $m> p \ge 2$, with isolated critical point. We show that this is satisfied by weighted-homogeneous maps. We also derive sufficient conditions in case of map germs with isolated critical value.