On two-dimensional holonomy

@article{Martins2010OnTH,
  title={On two-dimensional holonomy},
  author={J. Martins and R. Picken},
  journal={Transactions of the American Mathematical Society},
  year={2010},
  volume={362},
  pages={5657-5695}
}
  • J. Martins, R. Picken
  • Published 2010
  • Mathematics, Physics
  • Transactions of the American Mathematical Society
  • We define the thin fundamental categorical group P2(M,�) of a based smooth manifold (M,�) as the categorical group whose objects are rank-1 homotopy classes of based loops on M, and whose morphisms are rank2 homotopy classes of homotopies between based loops on M. Here two maps are rank-n homotopic, when the rank of the differential of the homotopy between them equals n. Let C(G) be a Lie categorical group coming from a Lie crossed module G = (∂: E ! G, ⊲). We construct categorical holonomies… CONTINUE READING
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