to 17/05/2024
Homology growth in topology and group theory


Homology growth is an umbrella term for a number of invariants associated to a topological space. In their simplest incarnation, they measure the growth of Betti numbers in finite covers of the space. Over the years, homology growth became a central topic in group theory and geometric topology. It connects various topological and geometric phenomena, especially in low-dimensional manifolds, with analytically or combinatorially defined invariants, like L^2-Betti numbers. In particular, homology growth plays a central role in controlling the existence of fiberings, over the circle in the topological setting, and over the integers in the algebraic one. The motivation and guiding principles come from the theory of 3-manifolds.Inspired by Agol's resolution of Thurston's Virtual Fibering Conjecture, homology growth and related ideas have been very recently used both in the algebraic setting of cubulated groups, and in higher dimensional negatively curved manifolds. This conference aims to bring together people behind these recent developments, provide an overview of the field and help formulate a coherent system of conjectures to guide us in the years to come.


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