1998/10/18 by Michael Färber, Michael Farber, Farber, Michael
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Mathematical Physics (math-ph) #Random Matrices and Applications #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics #Symplectic Geometry (math.SG) #math-ph #math.AT #math.DG #math.MP #math.RT #math.SG
paper · pdf · doi:10.48550/arxiv.math/9810114
9 pages
arxiv created 1998/10/18 · openalex publication_date 1998/10/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that the Novikov inequalities for critical points of closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a corollary we obtain a vanishing theorem for L2 cohomology, generalizing a theorem of W. Lueck. We also prove that von Neumann Betti numbers coincide with the Novikov numbers for free abelian coverings.