A construction of associative submanifolds near the singular limit

Daniel Platt, King's College London

Associative submanifolds are certain 3-dimensional manifolds in 7-dimensional manifolds. They are calibrated, and therefore minimal surfaces, and there is a research programme that attempts to count them in order to define numerical invariants of manifolds, similar to Gromov-Witten invariants. However, not many examples of associative submanifolds are known, which is one of the difficulties in working out the details of this programme. In the talk I will explain how to construct some dozens of associatives whose existence had previously been predicted by physicists. They are different from all previously known associatives in that their volume goes to zero as the ambient manifold converges to a certain singular limit.

MC 5417