Von Neumann Betti numbers and Novikov type inequalities
نویسندگان
چکیده
منابع مشابه
Von Neumann Betti Numbers and Novikov Type Inequalities
In this paper we show that Novikov type inequalities for closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a consequence we obtain a vanishing theorem for L cohomology. We also prove that von Neumann Betti numbers coincide with the Novikov numbers for free abelian coverings. §0. Introduction S. Novikov and M. Shubin [NS] proved that Morse inequalities for ...
متن کاملNovikov-betti Numbers and the Fundamental Group
This result may appear striking as the Novikov-Betti numbers carry “abelian” information about X. We refer to [4], [3] for the definition of the Novikov-Betti numbers; an explicit definition will also be given below in the proof of Theorem 1. An alternative description of bi(ξ) uses homology of complex flat line bundles. Consider the variety Vξ of all complex flat line bundles L over X having t...
متن کاملL 2 - Topological Invariants of 3 - manifolds by John Lott and Wolfgang Lück
We give results on the L2-Betti numbers and Novikov-Shubin invariants of compact manifolds, especially 3-manifolds. We first study the Betti numbers and Novikov-Shubin invariants of a chain complex of Hilbert modules over a finite von Neumann algebra. We establish inequalities among the Novikov-Shubin invariants of the terms in a short exact sequence of chain complexes. Our algebraic results, a...
متن کاملA Hierarchy of Von Neumann Inequalities?
The well-known von Neumann inequality for commuting row contractions can be interpreted as saying that the tuple (Mz1 , . . . ,Mzn) on the Drury-Arveson space H 2 n dominates every other commuting row contraction (A1, . . . , An). We show that a similar domination relation exists among certain pairs of “lessor” row contractions (B1, . . . , Bn) and (A1, . . . , An). This hints at a possible hie...
متن کاملThe James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces
Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05340-5