Geometry/topology Seminar

The Singer conjecture in dimension three revisited and its extensions


Speaker(s): Luca Di Cerbo (University of Florida, Math)
In this talk, I will show how Price inequalities for harmonic forms combined with some standard topology and geometry of 3-manifolds imply the Singer conjecture in dimension three. This provides an alternative proof of a result of Lott and Lueck (Invent. Math., 1995). Finally, I will outline some possible generalizations of this new approach in higher dimensions.

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