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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].

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
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