Local invariants of singular surfaces in an almost complex four-manifold
type: Item
instance of: scholarly article
title: Local invariants of singular surfaces in an almost complex four-manifold
zbMATH Open document ID: 0831.57019
DOI: 10.1007/BF00773451
author: Toru Ohmoto
author: Goo Ishikawa
published in: Annals of Global Analysis and Geometry
publication date: 1995-03-01T00:00:00Z
review text: Let \(f: S^2\to (M^4, J)\) be a generic mapping, that is, \(f\) is a finite cover of an almost everywhere immersion (except for a finite number of points) which has only finite complex points. To such a mapping \(f\) the authors assign local invariants \(i(x)\) and \(m(x)\) at every point \(x\in f (S^2)\). The invariant \(i(x)\) is defined as the local intersection number of \(V\) and its canonical perturbation \(V'\) around \(x\) (an idea of McDuff in her paper on local behaviour of pseudo-holomorphic curves in symplectic 4-manifolds), and the invariant \(m(x)\) is a generalization of the Maslov index by Givental (for Lagrangian embedding in symplectic 4-manifolds). The authors obtain formulae relating these local invariants at singular points of \(f\) and topological invariant of \(V\) (through Euler class, first Chern class and self-intersection number).
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 727084
zbMATH Keywords: singular immersion
zbMATH Keywords: pseudo-holomorphic curves in symplectic 4-manifolds
zbMATH Keywords: Maslov index
zbMATH Keywords: Lagrangian embedding in symplectic 4-manifolds
zbMATH Keywords: singular points
zbMATH Keywords: Euler class
zbMATH Keywords: Chern class
zbMATH Keywords: self-intersection number
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 727084