The fundamental crossed module of the complement of a knotted surface

DOI10.1090/S0002-9947-09-04576-0zbMath1200.57014arXiv0801.3921MaRDI QIDQ3394969

João Faria Martins

Publication date: 11 September 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.3921

zbMATH Keywords

crossed moduleshomotopy 2-typesKnotted surfaces

Mathematics Subject Classification ID

Related Items (9)

Surface holonomy for non-Abelian 2-bundles via double groupoids ⋮ Minimal generating sets of moves for surfaces immersed in the four-space ⋮ Categorifying the Knizhnik-Zamolodchikov connection ⋮ Pointed homotopy and pointed lax homotopy of 2-crossed module maps ⋮ Higher lattices, discrete two-dimensional holonomy and topological phases in (3 + 1)D with higher gauge symmetry ⋮ The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module ⋮ Cohomology with local coefficients and knotted manifolds ⋮ On a canonical lift of Artin's representation to loop braid groups ⋮ Homotopy 2-Types of Low Order

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonabelian algebraic topology. Filtered spaces, crossed complexes, cubical homotopy groupoids. With contributions by Christopher D. Wensley and Sergei V. Soloviev
• On Dehn's lemma and the asphericity of knots
• On the homotopy type and the fundamental crossed complex of the skeletal filtration of a CW-complex
• k-invariants of knotted 2-spheres
• Free simplicial groups and the second relative homotopy group of an adjunction space
• Crossed \(n\)-fold extensions of groups and cohomology
• Colimit theorems for relative homotopy groups
• The homotopy groups of knots. I: How to compute the algebraic 2-type
• Spaces with finitely many non-trivial homotopy groups
• The topology of 4-manifolds
• Combinatorial homotopy and 4-dimensional complexes
• On 2-dimensional CW-complexes with a single 2-cell
• Groupoids and crossed objects in algebraic topology
• A combinatorial description of knotted surfaces and their isotopies
• An enumeration of surfaces in four-space
• Surfaces in 4-space
• Differential topology from the point of view of simple homotopy theory
• On adding relations to homotopy groups
• Cohomology theory in abstract groups. III. Operator homomorphisms of kernels
• Note on a previous paper entitled 'On adding relations to homotopy groups'
• The classifying space of a crossed complex
• Invariants of welded virtual knots via crossed module invariants of knotted surfaces
• On the Second Relative Homotopy Group of an Adjunction Space: An Exposition of a Theorem of J. H. C. Whitehead
• Homology of groups of surfaces in the 4-sphere
• Generalized Group Presentation and Formal Deformations of CW Complexes
• On the Connection between the Second Relative Homotopy Groups of Some Related Spaces
• Topological Quantum Field Theories from Homotopy n -Types
• INTERPRETATIONS OF YETTER’S NOTION OF G-COLORING: SIMPLICIAL FIBRE BUNDLES AND NON-ABELIAN COHOMOLOGY
• ON A CALCULUS FOR 2-KNOTS AND SURFACES IN 4-SPACE
• TQFT’S FROM HOMOTOPY 2-TYPES
• CATEGORICAL GROUPS, KNOTS AND KNOTTED SURFACES
• On the 3-Type of a Complex
• Combinatorial homotopy. II
• Determination of the Second Homology and Cohomology Groups of a Space by Means of Homotopy Invariants

This page was built for publication: The fundamental crossed module of the complement of a knotted surface