Novikov's Conjecture

TL;DR

This paper discusses Novikov's higher signature conjecture, a fundamental unsolved problem in high-dimensional topology, exploring its various formulations and its influence across multiple mathematical disciplines.

Contribution

It provides a comprehensive overview of Novikov's conjecture, including alternative formulations and its significance in diverse areas of mathematics.

Findings

Survey of different formulations of the conjecture

Analysis of its implications in geometry and operator algebras

Identification of related open problems

Abstract

We describe Novikov's "higher signature conjecture," which dates back to the late 1960's, as well as many alternative formulations and related problems. The Novikov Conjecture is perhaps the most important unsolved problem in high-dimensional manifold topology, but more importantly, variants and analogues permeate many other areas of mathematics, from geometry to operator algebras to representation theory