ON A CALCULUS FOR 2-KNOTS AND SURFACES IN 4-SPACE

DOI10.1142/S0218216501001359zbMath1001.57044OpenAlexW2078514381MaRDI QIDQ4541064

Frank J. Swenton

Publication date: 30 July 2002

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218216501001359

zbMATH Keywords

moving pictures

Mathematics Subject Classification ID

Embeddings in differential topology (57R40)

Related Items (29)

Applying Lipson's state models to marked graph diagrams of surface-links ⋮ Computations of quandle cocycle invariants of surface-links using marked graph diagrams ⋮ On invariants for surface-links in entropic magmas via marked graph diagrams ⋮ Surface-knots ⋮ On the Alexander biquandles of oriented surface-links via marked graph diagrams ⋮ Polynomial of an oriented surface-link diagram via quantum \(A_2\) invariant ⋮ On a surface singular braid monoid ⋮ Bridge trisections of knotted surfaces in 𝑆⁴ ⋮ Polynomial invariants for virtual marked graphs and virtual surface-link theory I ⋮ Tri-plane diagrams for simple surfaces in S4 ⋮ Minimal generating sets of moves for surfaces immersed in the four-space ⋮ INVARIANTS OF SURFACE LINKS IN ℝ⁴ VIA SKEIN RELATION ⋮ 2-Knot homology and Yoshikawa move ⋮ Independence of the Yoshikawa eighth move and a minimal generating set of band moves ⋮ The 4-dimensional light bulb theorem ⋮ All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron ⋮ Generalizations of a Conway algebra for oriented surface-links via marked graph diagrams ⋮ Isotopies of surfaces in 4-manifolds via banded unlink diagrams ⋮ Stabilization distance between surfaces ⋮ Towards invariants of surfaces in $4$-space via classical link invariants ⋮ Presentation of immersed surface-links by marked graph diagrams ⋮ Biquandle cohomology and state-sum invariants of links and surface-links ⋮ On a banded link presentation of knotted surfaces ⋮ Bikei invariants and gauss diagrams for virtual knotted surfaces ⋮ Minimal generating set of planar moves for surfaces embedded in the four-space ⋮ Minimal hard surface-unlink and classical unlink diagrams ⋮ The fundamental crossed module of the complement of a knotted surface ⋮ IDEAL COSET INVARIANTS FOR SURFACE-LINKS IN ℝ⁴ ⋮ On generating sets of Yoshikawa moves for marked graph diagrams of surface-links

Cites Work

• The homotopy groups of knots. I: How to compute the algebraic 2-type
• Five-dimensional knot theory
• REIDEMEISTER MOVES FOR SURFACE ISOTOPIES AND THEIR INTERPRETATION AS MOVES TO MOVIES

This page was built for publication: ON A CALCULUS FOR 2-KNOTS AND SURFACES IN 4-SPACE