Topology and Geometric Group Theory Seminar

Alyson BittnerSUNY Buffalo
Spaces with complexity one

Tuesday, March 21, 2017 - 1:30pm
Malott 203

The inductive construction of a $CW$-complex builds the space out of spheres. This process can be generalized to build $A$-cellular spaces out of some fixed space $A$. Given such a construction, we can ask if it is the most efficient construction in the sense that it requires the least ordinal number of steps to build the space out of copies of $A$, called the $A$-complexity. With certain assumptions on $A$, every space has $A$-complexity less than or equal to one. We will discuss the properties and significance of such spaces $A$ with the use of algebraic theories.