Open Problems in Mathematics

2015/06/17 by John F. Nash, Jonathan Rosenberg, Michael Th. Rassias · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Mathematical Approximation and Integration #Mathematics #Mathematics education #Polynomial and algebraic computation #Quantum chaos and dynamical systems #math.AT #math.KT #msc:19D50 #msc:19G24 #msc:19J25 #msc:19K56 #msc:57R67 #msc:58J22

paper · pdf · doi:10.1007/978-3-319-32162-2

published as "Open Problems in Mathematics", J. F. Nash, Jr., and M. Th. Rassias, eds, Springer, 2016, pp. 377-402 · 22 pages

arxiv created 2015/06/17 · openalex publication_date 2016/01/01 · arxiv updated 2016/08/16 · openalex created_date 2022/09/16 · openalex updated_date 2026/07/21

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

Citations

• The coarse Baum–Connes conjecture and groupoids
• Modifications and Cobounding Manifolds

Cited by

• Architectures for Quantum Simulation Showing a Quantum Speedup
• John Forbes Nash Jr. [wikipedia]

Related

• Elliptic Operators and Higher Signatures
• Signatures and Higher Signatures of S¹-Quotients
• The Novikov conjecture on Cheeger spaces
• HyperEuclidean manifolds and the Novikov Conjecture
• A glimpse into Rokhlin's Signature Divisibility Theorem