Finite domination, Novikov homology and nonsingular closed 1-forms
type: Item
instance of: scholarly article
title: Finite domination, Novikov homology and nonsingular closed 1-forms
zbMATH Open document ID: 1094.57024
published in: Mathematische Zeitschrift
publication date: 2006-03-21T00:00:00Z
review text: Let \(M\) be a closed connected smooth manifold of dimension at least 6. This paper considers the question of realizing a nonzero homomorphism \(\xi: \pi_1(M) \rightarrow \mathbb{R}\) by a nonsingular closed 1-form. The main result is that if \(N \subset \pi_1(M)\) is a normal subgroup with \(\pi_1(M)/N = \mathbb{Z}^k\) and the covering space corresponding to \(N\) is finitely dominated, then homomorphisms \(\xi\) with kernel contained in \(N\) are either all realized or none is realized.
Mathematics Subject Classification ID: 57R19
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 5013688
author: Dirk Schütz
MaRDI profile type: Publication
full work available at URL: s00209-005-0868-8
OpenAlex ID: W2029186238
cites work: Valuations on free resolutions and higher geometric invariants of groups
cites work: Formes fermées non singulières et propriétés de finitude des groupes
cites work: Zeros of closed 1-forms, homoclinic orbits and Lusternik-Schnirelman theory.
cites work: Q5653385
cites work: Trace and torsion in the theory of flows
cites work: Q4716270
cites work: Existence of nonsingular closed 1-forms in a de Rham cohomology class
cites work: Counting homotopy types of manifolds
cites work: Whitehead torsion
cites work: The Whitehead group of the Novikov ring
cites work: The algebraic theory of finiteness obstruction.
cites work: Finite domination and Novikov rings
cites work: Q4210473
cites work: The algebraic construction of the Novikov complex of a circle-valued Morse function
cites work: A total Whitehead torsion obstruction of fibering over the circle
cites work: On fibering certain foliated manifolds over \(S^1\)
cites work: Finiteness conditions for CW-complexes. I, II.
DOI: 10.1007/S00209-005-0868-8
Recommended article: Finite domination and Novikov rings
Recommended article: Finite domination and Novikov homology over strongly \(\mathbb{Z}\)-graded rings
Recommended article: FINITE DOMINATION AND NOVIKOV RINGS. ITERATIVE APPROACH
Recommended article: Homological domino effects and the first finitistic dimension conjecture
Recommended article: Homotopy dominations by polyhedra with polycyclic-by-finite fundamental groups
Recommended article: Finiteness obstructions for homologically nilpotent spaces
Recommended article: The Novikov conjecture and low-dimensional topology
Recommended article: Q4207389
Recommended article: Almost finiteness and homology of certain non-free actions
Recommended article: Domination numbers and homology
description: scientific article; zbMATH DE number 5013688