Geometry Colloquium: On the topological complexity of spaces with nontrivial fundamental groups (箕輪悠希)

Time： 16:30-17:30

Place：Faculty of Science Building  #3, Room 204

Speaker：箕輪悠希（京都大学）

Title：On the topological complexity of spaces with nontrivial fundamental groups

Abstract：Topological complexity is a numerical homotopy invariant that measures the instability of motion planning in a space. To study the topological complexity of non-simply connected spaces, Costa and Farber introduced a canonical cohomology class, which provides both upper and lower bounds. In this talk, I will survey recent developments in this direction, with particular emphasis on the spectral sequence approach developed by Farber and Mescher. I will then show that this spectral sequence is natural with respect to group homomorphisms. Finally, I will also discuss some computational examples that follow from this naturality.