From finiteness properties to polynomial filling via homological algebra

Abstract: If a group has type $\textrm{FP}_n$ one can define higher filling functions, which give a quantitative refinement of $\textrm{FP}_n$ by measuring the size of fillings of $k$‑cycles ($k \leq n$). We develop a homological‑algebra framework that extends existing tools for finiteness properties to produce polynomial bounds for these filling functions. The goal is to make deducing polynomiality as straightforward as proving $\textrm{FP}_n$.

This is based on joint work with Roman Sauer.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.