Real and complex line fields on manifolds

Baylee Schutte (University of Aberdeen)

Monday 18th November 16:00-17:00 Maths 311B

Abstract

The projective span of a smooth manifold is the maximal number of linearly independent line fields. First, I will define this numerical invariant and motivate its study. Second, from work joint with Mark Grant, I will explain our calculation of the projective span of all of the Wall manifolds (which are real manifolds of longstanding interest in differential topology). Third, from recently finished work joint with Nikola Sadovek, I will identify complete obstructions to the existence of 1, 2, or 3 linearly independent complex line fields on certain classes of almost-complex manifolds and give some examples.

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