Symplectic Torelli groups for positive rational surfaces

Abstract: Donaldson (folklore) asked whether Lagrangian Dehn twists always generate the symplectic mapping class groups in real dimension four. So far, all known examples indicate this is true, even though the symplectic Torelli group is generally much larger than the algebraic one. Yet there are only very few cases people could prove this as a theorem.

We will define a notion of "positive rational surfaces", which is equivalent to the ambient symplectic manifolds of (symplectic) log Calabi-Yau pairs. We compute the symplectic Torelli group for the positive rational surfaces and confirm Donaldson's conjecture as a result. We also answer several other questions about the symplectic Torelli groups in dimension $4$.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

Series comments: To receive the series announcements, which include the
Zoom access password*, please register in
math.tecnico.ulisboa.pt/seminars/geolis/index.php?action=subscribe#subscribe
*the last announcement for a seminar is sent 2 hours before the seminar.

Geometria em Lisboa video channel: educast.fccn.pt/vod/channels/bu46oyq74