Combinatorial and Gauge theoretical methods in low dimensional topology and geometry

Lens spaces in the complex projective plane, II: constructions

speaker: Brendan Owens (University of Glasgow)

abstract: Which lens spaces embed smoothly in the complex projective plane, and which collections of lens spaces can be disjointly embedded? Work of Manetti and Hacking-Prokhorov showed that each solution to the Markov equation gives rise to a triple of lens spaces which embed disjointly, and Evans-Smith showed this accounts for all symplectic embeddings of the standard rational homology balls bounded by these lens spaces. Further embeddings of lens spaces have since been exhibited, including two families of triples which embed disjointly due to Lisca-Parma.

I will exhibit some new triples of examples, and will show in particular that all lens spaces L(p^2,pq-1) with gcd(p,q)=2, or with p odd and gcd(p,q)=1, embed in CP^2.

This is joint work with Marco Golla.

timetable:
Thu 6 Jun, 11:00 - 12:00, Aula Dini
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