On the normal cycles of subanalytic sets

TL;DR

This paper provides a concise proof demonstrating the existence of the normal cycle for compact subanalytic sets, utilizing Morse theory and o-minimal topology inspired by Joseph Fu's ideas.

Contribution

It offers a complete, simplified proof of the normal cycle existence for subanalytic sets, combining Morse theory with o-minimal topology techniques.

Findings

Established the existence of the normal cycle for compact subanalytic sets.

Introduced a new proof approach inspired by Joseph Fu's ideas.

Utilized Morse theory and o-minimal topology in the proof.

Abstract

We present a short complete proof of the existence of the normal cycle of a compact subanalytic set. The approach is inspired by some old ides of Joseph Fu, uses Morse theoretic techniques and $o$-minimal topology.