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Scalable spaces

Posted in
Fedor Manin
University of California, Santa Barbara
Thu, 27/05/2021 - 18:30 - 20:00

Please note the time.

The seminar is virtual via Zoom. If you are interested in participating, please contact Stephan Stadler  (stadler@mpim-bonnmpgde)

A closed $n$-manifold is \emph{scalable} if it has
asymptotically maximally efficient self-maps: $O(d^{1/n})$-Lipschitz maps
of degree $d$, for infinitely many $d$.  For example, spheres and tori are
scalable, but surfaces of higher genus are not.  Simply connected manifolds
that don't have a cohomological obstruction to scalability are called
\emph{formal}, an idea introduced by Sullivan.  In joint work with
Berdnikov, we show that certain formal spaces are nevertheless not
scalable, and give several equivalent conditions for scalability.  For just
one example, $(CP^2)^{\#3}$ is scalable but
$(CP^2)^{\#4}$ is not.

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