Scalable spaces

Fedor Manin
University of California, Santa Barbara
Thursday, April 22, 2021 - 3:30pm to 4:30pm
Zoom ID 91514486597 (contact faculty for pw)

I will discuss topological invariants arising in metric geometry. In the 1970s, Gromov remarked that the n-sphere has self-maps of degree L^n whose Lipschitz constant is O(L), for every integer L. These should be thought of as maps of maximal geometric efficiency; we say a closed n-manifold is scalable if it admits efficient self-maps in infinitely many degrees. How can we decide which manifolds are scalable? Recently, Sasha Berdnikov and I showed that for simply connected manifolds, scalability is an invariant of rational homotopy type, and gave some equivalent conditions. For example, we found that the connected sum of three CP^2's is scalable but the connected sum of four is not.