Groupoids and crossed objects in algebraic topology.
Groupoids, the Phragmen-Brouwer property, and the Jordan curve theorem.
Algebraic colimit calculations in homotopy theory using fibred and cofibred categories.
Cubical Abelian groups with connections are equivalent to chain complexes.
Double categories, 2-categories, thin structures and connections.
On infinite induced crossed modules and the homotopy 2-type of mapping cones.
Computing crossed modules induced by an inclusion of a normal subgroup, with applications to homotopy 2-types.
Connections, local subgroupoids, and a holonomy Lie groupoid of a line bundle gerbe.
Q-perfect groups and universal Q-central extensions.
Using results of Ellis-Rodríguez Fernández, an explicit description by generators and relations is given of the mod q Schur multiplier, and this is shown to be the kernel of a universal q-central extension in the case of a q-perfect group, i.e. one which is generated by commutators and q-th powers. These results generalise earlier work [by] K. Dennis and Brown-Loday.
Three themes in the work of Charles Ehresmann: local-to-global; groupoids; higher dimensions
This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored.
A homotopy double groupoid of a Hausdorff space.
Algebraic topology foundations of supersymmetry and symmetry breaking in quantum field theory and quantum gravity: a review.
A homotopy double groupoid of a Hausdorff space. II: A van Kampen theorem.
Exponential laws for topological categories, groupoids and groups, and mapping spaces of colimits
Foliations, locally Lie groupoids and holonomy
A model structure for the homotopy theory of crossed complexes
The monodromy groupoid of a Lie groupoid
Coglueing Homotopy Equivalences.
The Homotopy Groups of an n-Fold Wedge.
Embeddings in contractible or compact objects
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