Algebraic monodromy and obstructions to formality

Abstract

Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more general result about iterated group extensions. As an application, we obtain new criteria for formality of spaces, and 1-formality of groups, illustrated by bundle constructions and various examples from low-dimensional topology and singularity theory.

10 pages, 1 figure; accepted for publication in Forum Mathematicum

References in corpus (5)

• Topology and geometry of cohomology jump loci
• The spectral sequence of an equivariant chain complex and homology with local coefficients
• Algebraic invariants for Bestvina-Brady groups
• Cohomology rings and formality properties of nilpotent groups
• Cohomology algebra of plane curves, weak combinatorial type, and formality

Cited by in corpus (6)

• The spectral sequence of an equivariant chain complex and homology with local coefficients
• Geometric and algebraic aspects of 1-formality
• Finite Galois covers, cohomology jump loci, formality properties, and multinets
• The monodromy theorem for compact Kähler manifolds and smooth quasi-projective varieties
• Cohomology jump loci of 3-manifolds
• On Kahler extensions of abelian groups