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.

# Branched surfaces in 4-manifolds

Please note this event occured in the past.

April 16, 2024 4:00 pm - 4:00 pm ET