Ross Geoghegan, Binghamton University (SUNY)

Thursday, January 31, 2019 - 2:30pm to 3:30pm

LOW 116

In this expository talk I will

1. introduce Thompson’s Group \$F\$, a famous finitely generated group.

2. explain the general concept of quasi-isometry of finitely generated groups;

3. state an unsolved problem, namely: is F quasi-isometric to \$F \times Z\$?

4. explain why this is an infinite-dimensional or “phantom map” type of problem so that ordinary invariants will not detect the difference between the two groups (if there is a difference).

If time permits, I will discuss two older problems in geometric topology which exhibit some similarities to this one, and which needed reduced complex K-theory or the Sullivan Conjecture for their solution.