Homotopy invariance of higher signatures
نویسنده
چکیده
We prove that the higher signature for any close oriented manifold is a homotopy invariant. 2000 MR Subject Classification 57N70, 57R95, 57R40
منابع مشابه
Elliptic Operators and Higher Signatures
Building on the theory of elliptic operators, we give a unified treatment of the following topics: • the problem of homotopy invariance of Novikov’s higher signatures on closed manifolds; • the problem of cut-and-paste invariance of Novikov’s higher signatures on closed manifolds; • the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.
متن کاملJ un 2 00 4 ELLIPTIC OPERATORS AND HIGHER SIGNATURES
Building on the theory of elliptic operators, we give a unified treatment of the following topics: • the problem of homotopy invariance of Novikov's higher signatures on closed manifolds; • the problem of cut-and-paste invariance of Novikov's higher signatures on closed manifolds; • the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.
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We show that for each discrete group Γ, the rational assembly map K∗(BΓ)⊗Q→ K∗(C maxΓ)⊗Q is injective on classes dual to Λ∗ ⊂ H∗(BΓ;Q), where Λ∗ is the subring generated by cohomology classes of degree at most 2. Our result implies homotopy invariance of higher signatures associated to classes in Λ∗. This consequence was first established by Connes-Gromov-Moscovici [4] and Mathai [9]. Our appro...
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The theorem of Novikov [21], that the rational Pontrjagin classes of a smooth manifold are invariant under homeomorphisms, was a landmark in the development of the topology of manifolds. The geometric techniques introduced by Novikov were built upon by Kirby and Siebenmann [19] in their study of topological manifolds. At the same time the problem was posed by Singer [30] of developing an analyt...
متن کاملThe Asymptotic Method in the Novikov Conjecture
The famous Hirzebruch signature theorem asserts that the signature of a closed oriented manifold is equal to the integral of the so called L-genus. An immediate corollary of this is the homotopy invariance of < L(M); [M ] >. The L-genus is a characteristic class of tangent bundles, so the above remark is a non-trivial fact. The problem of higher signatures is a generalization of the above consi...
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تاریخ انتشار 2009