Combining Papasoglu's trick with simplicial volume

Venue:
20.30, SR 1.058, via Zoom

Date:
04.05.2023
 Speaker:

Time:
15:45

Abstract: In 1983 Gromov proved the systolic inequality: if M is a closed, essential ndimensional Riemannian manifold where every loop of length 2 is nullhomotopic, then the volume of M is at least a constant depending only on n. He also proved a version that depends on the simplicial volume of M, saying that if the simplicial volume is large, then the lower bound on volume becomes proportional to the simplicial volume divided by the nth power of its logarithm. Nabutovsky showed in 2019 that Papasoglu's method of areaminimizing separating sets recovers the systolic inequality and improves its dependence on n. We introduce simplicial volume to the proof, recovering the statement that the volume is at least proportional to the square root of the simplicial volume.