The coarse geometric Novikov conjecture and uniform convexity
Gennadi Kasparov,Guoliang Yu +1 more
TLDR
In this paper, the coarse geometric Novikov conjecture for spaces which admit a uniform embedding into a uniformly convex Banach space was proved for the case of uniform embeddings.About:
This article is published in Advances in Mathematics.The article was published on 2006-10-20 and is currently open access. It has received 106 citations till now. The article focuses on the topics: Novikov conjecture & Banach space.read more
Citations
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Metric Geometry of Locally Compact Groups
TL;DR: In this paper, the authors study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study infinite groups as geometric objects, as Gromov writes it in the title of a famous article.
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Metric Cotype
Manor Mendel,Assaf Naor +1 more
TL;DR: This property of metric cotype is used to prove the following dichotomy: A family of metric spaces F is either almost universal (i.e., contains any finite metric space with any distortion > 1), or there exists α > 0, and arbitrarily large (F) is at least Ω((log )α).
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Un renforcement de la propriété (T)
TL;DR: In this article, a strong form of property (T) for real or p-adic semisimple groups is shown, where the trivial representation is isolated among representations with a small exponential growth in Hilbert spaces or even in uniformly convex Banach spaces.
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Decomposition of homogeneous polynomials with low rank
TL;DR: In this article, a homogeneous polynomial of degree d in m+1 variables defined over an algebraically closed field of characteristic 0 was shown to have a minimal decomposition as a sum of d-th powers of linear forms.
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Some notes on Property A
TL;DR: In this article, the authors provide an expository account of Guoliang Yu's property A. The piece starts from the basic definitions, and goes on to discuss closure properties of the class of property A spaces and groups.
References
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Geometry of Banach Spaces - Selected Topics
TL;DR: Support functionals for closed bounded convex subsets of a Banach space are studied in this article, where the classical renorming theorems for the Radon-Nikodym theorem for vector measures are discussed.
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Positive scalar curvature and the Dirac operator on complete riemannian manifolds
TL;DR: Theoreme d'indice relatif as mentioned in this paper generalises sur a complete variete complete and generalizes on varietes incompletes of dimension ≤ 7, which represent classes d'homologie non triviales dans des espaces de courbure non positive.
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The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space
TL;DR: The strong Novikov conjecture on the homotopy invariance of higher signatures was shown to hold for finite CW complex groups in this paper, i.e., the index map from K ∗(BΓ) to K∗(C∗ r (Γ)) is injective.