Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds

DOI10.1002/cpa.21962zbMath1476.57044arXiv1608.03661OpenAlexW3096310770MaRDI QIDQ4995549

Zhizhang Xie, Shmuel Weinberger, Guo-Liang Yu

Publication date: 25 June 2021

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.03661

zbMATH Keywords

\(C^*\)-algebra\(K\)-theoryhigher rho invariantPoincaré complextopological manifold

Mathematics Subject Classification ID

Algebraic topology of manifolds (57N65) Index theory (19K56) Surgery obstructions ((K)-theoretic aspects) (19J25)

Related Items (15)

Delocalized Eta Invariants, Algebraicity, and K-Theory of Group C*-Algebras ⋮ Functoriality for higher rho invariants of elliptic operators ⋮ On the cardinality of the manifold set ⋮ Topological \(K\)-theory for discrete groups and index theory ⋮ Delocalized eta invariants, cyclic cohomology and higher rho invariants ⋮ \(K\)-theory of relative group \(C^*\)-algebras and the relative Novikov conjecture ⋮ On the relative \(L\)-theory and the relative signature of PL manifolds with boundary ⋮ Approximations of delocalized eta invariants by their finite analogues ⋮ Interior Kasparov products for \(\varrho\)-classes on Riemannian foliated bundles ⋮ Secondary higher invariants and cyclic cohomology for groups of polynomial growth ⋮ Higher invariants in noncommutative geometry ⋮ The Novikov conjecture ⋮ The adiabatic groupoid and the Higson-Roe exact sequence ⋮ On localized signature and higher rho invariant of fibered manifolds ⋮ Slant products on the Higson-Roe exact sequence

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