Homotopy theory of lattices
Constanze Roitzheim (University of Kent)
Monday 19th January 15:00-16:00
Maths 311B
Abstract
A transfer system is a graph on a lattice satisfying certain restriction and composition properties. They were first studied on the lattice of subgroups of a finite group in order to examine equivariant homotopy commutativity, which then unlocked a wealth of links to combinatorial methods.
On a finite lattice, transfer systems can be used to classify different homotopy theories using model categories. This means that some often complicated homotopy information can now be encoded in simple, combinatorial terms, which makes model categories much easier to access and handle. The talk will involve plenty of examples and not assume any background knowledge.
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