Rosenberg, Jonathan Novikov’s conjecture. (English) Zbl 1350.57034 Nash, John Forbes jun. (ed.) et al., Open problems in mathematics. Cham: Springer (ISBN 978-3-319-32160-8/hbk; 978-3-319-32162-2/ebook). 377-402 (2016). Summary: We describe Novikov’s “higher signature conjecture,” which dates back to the late 1960s, 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.For the entire collection see [Zbl 1351.00027]. Cited in 4 Documents MSC: 57R67 Surgery obstructions, Wall groups 57R20 Characteristic classes and numbers in differential topology 19J25 Surgery obstructions (\(K\)-theoretic aspects) 57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010) 57-03 History of manifolds and cell complexes 01A60 History of mathematics in the 20th century PDFBibTeX XMLCite \textit{J. Rosenberg}, in: Open problems in mathematics. Cham: Springer. 377--402 (2016; Zbl 1350.57034) Full Text: DOI References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.