[Binghamton Geometry Topology Seminar] Geometry and Topology seminar this week

[Cary Malkiewich]

Hi everyone,

This week we have our very own Daniel Studenmund talking about
solenoids, title and abstract below. As usual, the talk will be on Thursday
at 2:50pm in WH 100E.

Anyone interested in going to lunch around 12pm that day, let me know! It
looks like it's possible to eat outside C4, though the doors lock and you
can't get back in. So no seconds.

Best,
Cary

Title: Homotopy equivalences of full solenoids
Abstract: Solenoids, inverse limits of self-coverings of the circle, are
important examples of compact connected metrizable spaces. They were
studied by topologists Mayer and van Dantzig, and arise in the theory of
hyperbolic dynamical systems as the Smale-Williams attractor. We will use
ideas from shape theory to show that homotopy equivalences of a solenoid
naturally correspond to certain rational numbers. The full solenoid over a
space X is the inverse limit of -all- finite covers of X. We will state a
generalization of the 1-dimensional result, relating homotopy equivalences
of the full solenoid over a finite CW complex X to isomorphisms between
finite-index subgroups of pi_1(X). If time permits, we will say a word on
the Teichmuller theory of the full solenoid over a closed hyperbolic
surface.
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