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Topology Seminar: The Thom conjecture in CP^3

Danny Ruberman

The homology groups of a smooth projective complex hypersurface in CP^n are determined by the degree of its defining equation. A question attributed to René Thom asks whether there is a smooth submanifold of CP^n with the same degree but with smaller Betti numbers. Kronheimer and Mrowka famously proved that the degree d curve in CP^2 has minimal Betti numbers, while Freedman showed many years ago that when n is even and at least4, the hypersurface does not minimize the Betti numbers. We show that this continues to hold when n = 3, finding smooth 4-manifolds embedded in CP^3 with degree at least 5 with b_2 smaller than the hypersurface of degree d.

This is joint work with Sašo Strle and Mark Slapar.

Monday, October 25 at 2:30pm

CW 122, CW 122

Event Type

Lecture, Colloquia, Seminar

Audience

Current students, Faculty

Department
Mathematics, Department of
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