Topology Seminar (Main Talk): Harmonic surfaces and simple loops

Seminar | January 30 | 4-5 p.m. | 3 Evans Hall | Canceled

 Vlad Markovic, Cal Tech

 Department of Mathematics

Fix a suitable (non-elementary) map $f$ from a closed surface $S$ into a closed hyperbolic 3-manifold $M$, and consider the moduli space of harmonic maps homotopic to $f$ and with respect to varying metrics on $S$ and $M$ (the metrics on $M$ are assumed to be negatively curved). We show that the set of such metrics for which the corresponding harmonic map is in Whitney's general position is an open, dense, and connected subset of this moduli space. One application of this result is the proof of the special case of the Simple Loop conjecture when $M$ is hyperbolic.