Algebra Seminar

The origin of pictures [POSTPONED]

Kiyoshi Igusa (Brandeis University)

Wednesday, March 7, 2018 11:15 am
MONT 313

Gordana Todorov, Jerzy Weyman, Kent Orr and I are working on a book about ``pictures'' which have gained renewed attention because they are equivalent to ``scattering diagrams''. This talk is about very old work that I did to introduce pictures and their relation to the cohomology of $\mathrm{GL}(n,\mathbb Z)$. In particular, I will discuss the pictures below (from our book!) and their relationship to $H^3(\mathrm{GL}(n,\mathbb Z),\mathbb Z/2)$.

The algebraic side of this story is a fun topic. The cohomology class which detects the ``exotic element'' of $K_3(\mathbb Z)$ is the degree 3 class which counts the number of times (modulo 2) that commutativity of addition is used to prove that matrix multiplication is associative! This is an old result which I am happy to present in a new light.