A glimpse into Rokhlin's Signature Divisibility Theorem

TL;DR

This paper reviews Rokhlin's proof of the signature divisibility theorem, discusses its historical development, and highlights its significance in modern manifold theory.

Contribution

It provides a comprehensive overview of Rokhlin's proof and traces the theorem's influence on contemporary manifold topology.

Findings

Rokhlin's theorem proves signature divisibility by 16.

Historical analysis of the theorem's development.

Its foundational role in modern manifold theory.

Abstract

This paper was conceived as an addendum to the note "Rokhlin's signature theorems" (by O.Viro and the authors of this paper). In the main section we give an overview of Rokhlin's proof of his famous theorem on divisibility of signature by 16. In the appendix we retrace some of further developments that show how this theorem became a cornerstone in the contemporary theory of manifolds.