E_2 algebras and homology - 2 of 2

Soren Galatius
Thu, Jun 13, 2019
PIMS, University of British Columbia
Workshop on Arithmetic Topology
Block sum of matrices define a group homomorphism GL_n(R) \times GL_m(R) \to GL_{n+m}(R), which can be used to make the direct sum of H_s(BGL_t(R);k) over all s, t into a bigraded-commutative ring. A similar product may be defined on homology of mapping class groups of surfaces with one boundary component, as well as in many other examples of interest. These products have manifestations on various levels, for example there is a product on the level of spaces making the disjoint union of BGL_n(R) into a homotopy commutative topological monoid. I will discuss how it, and other concrete examples, may be built by iterated cell attachments in the category of topological monoids, or better yet E_2 algebras, and what may be learned by this viewpoint. This is all joint work with Alexander Kupers and Oscar Randal-Williams.


This is the second lecture in a two part series: part 1