Conic singularities and immediate transversality

TL;DR

This paper proves that immediate transversality, a concept previously introduced in Morse theory, holds for all compact submanifolds with $C^1$ conic singularities, extending its applicability beyond Morse complexes.

Contribution

It establishes that immediate transversality applies to all compact submanifolds with $C^1$ conic singularities, broadening the scope of the concept.

Findings

Immediate transversality holds for $C^1$ conic singularities.

Extension of transversality results beyond Morse theory.

Applicable to all compact submanifolds with conic singularities.

Abstract

I introduced the notion of immediate transversality in a recent paper on $A_\infty$-structures on Morse complexes. I the present chapter, I prove that immediate transversality holds for every compact submanifold with $C^1$ conic singularities, not only in the setup of Morse Theory. This is an occasion of speaking of this type of singularities.