Conic singularities and immediate transversality

Abstract

I introduced the notion of immediate transversality in a recent paper on $A_{\infty }$-structures on Morse complexes. In 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.