Generic immersions of curves, knots, monodromy and Gordian number

DOI10.1007/BF02701769zbMath0960.57007arXivmath/9803081OpenAlexW2169469219MaRDI QIDQ1594565

Norbert A'Campo

Publication date: 19 April 2001

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9803081

zbMATH Keywords

plane curvefibered link

Mathematics Subject Classification ID

Related Items (35)

Lagrangian skeleta and plane curve singularities ⋮ Links associated with generic immersions of graphs ⋮ Diagrams of divide links ⋮ Essential cycles in graph divides as a link representation ⋮ Divides with cusps and Kirby diagrams for line arrangements ⋮ On polynomials and surfaces of variously positive links ⋮ On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number ⋮ On the Lagrangian fillability of almost positive links ⋮ Genus generators and the positivity of the signature ⋮ Casson invariant of knots associated with divides ⋮ Expressive curves ⋮ Plumbing constructions of connected divides and the Milnor fibers of plane curve singularities ⋮ Morsifications and mutations ⋮ Singularities. Abstracts from the workshop held September 26 -- October 2, 2021 (hybrid meeting) ⋮ Invariants of transverse foliations ⋮ Unnamed Item ⋮ The link of an extrovert divide ⋮ A combinatorial property of generic immersions of curves ⋮ Curves on surfaces, charts, and words ⋮ A family of knots yielding graph manifolds by Dehn surgery. ⋮ BERGE'S KNOTS IN THE FIBER SURFACES OF GENUS ONE, LENS SPACE AND FRAMED LINKS ⋮ Presentations of periodic maps on oriented closed surfaces of genera up to 4 ⋮ Application of braiding sequences. IV: Link polynomials and geometric invariants ⋮ Some fibered and non-fibered links at infinity of hyperbolic complex line arrangements ⋮ Divide knot presentation of sporadic knots of Berge's lens space surgery ⋮ Signature, positive Hopf plumbing and the Coxeter transformation (With appendix by Peter Feller and Livio Liechti) ⋮ Lens space surgeries as A'Campo's divide knots ⋮ Lissajous curves as A'Campo divides, torus knots and their fiber surfaces ⋮ Real deformations and complex topology of plane curve singularities ⋮ First-return maps of Birkhoff sections of the geodesic flow ⋮ Quadratic vanishing cycles, reduction curves and reduction of the monodromy group of plane curve singularities ⋮ Application of braiding sequences III: Concordance of positive knots ⋮ Links and gordian numbers associated with generic immersions of intervals ⋮ Quasipositivity of links of divides and free divides ⋮ Visualization of A'Campo's fibered links and unknotting operation

Cites Work

• Le groupe de monodromie du déploiement des singularités isolées de courbes planes. I
• The unknotting numbers of \(10_{139}\) and \(10_{152}\) are 4
• Unknotting numbers of quasipositive knots
• Gauge theory for embedded surfaces. I
• Gauge theory for embedded surfaces. II
• Monopoles and contact structures
• Real deformations and complex topology of plane curve singularities
• Deformations of cones with negative grading
• The genus of embedded surfaces in the projective plane
• The Seiberg-Witten invariants and symplectic forms
• Embedded surfaces and the structure of Donaldson's polynomial invariants
• Die gordische Auflösung von Knoten
• On the Alexander polynomial
• The genus-minimizing property of algebraic curves
• Singular Points of Complex Hypersurfaces. (AM-61)
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