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Topological Quantum Field Theory Seminar   RSS

14/07/2005, 15:30 — 16:30 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Gerbes and their Parallel Transport

Gerbes are higher-order generalizations of Abelian bundles. They appear in nature, for instance as obstructions to lifting SO (n) -bundles to Spin (n) or Spin c (n) bundles. It is possible to endow gerbes with connection 1- and 2-forms and curvature 3-forms, and study aspects of the ensuing differential geometry. In particular, gerbes with connection have holonomies and parallel transports along surfaces, as opposed to along loops and paths. Apart from discussing these features, I hope to describe an interesting recent categorification approach to non-Abelian gerbes due to Baez and Schreiber.

References

  1. J. Baez and U. Schreiber, Higher gauge theory: 2-connections on 2-bundles, hep-th/0412325.
  2. M. Mackaay and R. Picken, Holonomy and parallel transport for Abelian gerbes, Adv. Math. 170, 287-339 (2002), math.DG/0007053.
  3. R. Picken, TQFT's and gerbes, Algebr. Geom. Topol. 4 (2004) 243-272, math.DG/0302065.

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Current organizers: José MourãoRoger Picken, Marko Stošić

Mathseminars

FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.

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