منابع مشابه
An Etale Approach to the Novikov Conjecture
We show that the rational Novikov conjecture for a group Γ of finite homological type follows from the mod 2 acyclicity of the Higson compactifcation of an EΓ. We then show that for groups of finite asymptotic dimension the Higson compactification is mod p acyclic for all p, and deduce the integral Novikov conjecture for these groups.
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...
متن کاملManifold aspects of the Novikov Conjecture
Many surveys have been written on the Novikov Conjecture. The goal here is to give an old-fashioned point of view, and emphasize connections with characteristic classes and the topology of manifolds. For more on the topology of manifolds and the Novikov Conjecture see [58], [47], [17]. This article ignores completely connections with C§-algebras (see the articles of Mishchenko, Kasparov, and Ro...
متن کاملHypereuclidean Manifolds and the Novikov Conjecture
We develop some basic Lipschitz homotopy technique and apply it to manifolds with finite asymptotic dimension. In particular we show that the Higson compactification of a uniformly contractible manifold is mod p acyclic in the finite dimensional case. Then we give an alternative proof of the Higher Signature Novikov Conjecture for the groups with finite asymptotic dimension. Finally we define a...
متن کاملManifold Aspects of the Novikov Conjecture 1975
be the Hirzebruch L-class of an oriented manifold M. Let B (or K(; 1)) denote any aspherical space with fundamental group. (A space is aspherical if it has a contractible universal cover.) In 1970 Novikov made the following conjecture. Many surveys have been written on the Novikov Conjecture. The goal here is to give an old-fashioned point of view, and emphasize connections with characteristic ...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2010
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.7912