Algebraic monodromy and obstructions to formality

Details Algebraic monodromy and obstructions to formality Algebraic monodromy and obstructions to formality

2008-12-31

arxiv.org/abs/0901.0105v2

Forum Mathematicum 22 (2010), no. 5, 973-983

Mathematics

Algebraic Topology

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

Scientific paper

10.1515/FORUM.2010.052

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.

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