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Branched surfaces in 4-manifolds

Event Category:
Reading Seminar on Automorphism Groups of Manifolds
Marina Ville
Université de Tours

In the 1980s, geometers studied the twistor degree of a surface S in a 4-manifold M, given by the sum of its tangent and normal bundles; TS and NS. A question arose: if a sequence (S_n) of immersed surfaces in M degenerates into a branched surface S_0; how does the twistor degree of S_0 compare with those of the S_n's? We go back to this problem and treat it locally around a branch point p of S_0. It amounts to comparing the amount of curvatures of TS_n and NS_n which concentrate close to p when n tends to infinity. We approach this question with topological tools (braids) rather than analytic ones and we give a few cases where an extra assumption, either geometric or topological, allows us to get some answers.

Tuesday, April 16, 2024 - 4:00pm
LGRT 1685