Milnor numbers for 2-surfaces in 4-manifolds
| dc.creator | Ville, Marina | |
| dc.date | 2007-01-30 | |
| dc.date.accessioned | 2026-07-07T07:44:03Z | |
| dc.date.available | 2026-07-07T07:44:03Z | |
| dc.description | In this paper (S_n) is a sequence of surfaces immersed in a 4-manifold which converges to a branched surface S_0. Up to sign, μ^T_p (resp. μ^N_p) will denote the amount of curvature of the tangent bundles TS_n (resp. the normal bundles NS_n) which concentrates around a singular point p of S_0 when n goes to infinity. By a slight abuse of notation, we call μ_p^T (resp. μ_p^N) the tangent (resp. normal) Milnor number of S_n at p. These numbers are not always well-defined; we discuss assumptions under which, if μ^T exists, then μ^N also exists and is smaller than -μ^T . When the second fundamental forms of the S_n's have a common L^2 bound, we relate μ^T and μ^N to a bubbling-off in the Grassmannian G_2^+(M). | |
| dc.identifier | https://arxiv.org/abs/math/0701896 | |
| dc.identifier | http://arxiv.org/abs/math/0701896 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123056 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C42 | |
| dc.title | Milnor numbers for 2-surfaces in 4-manifolds | |
| dc.type | text |