20/05/2020, 17:00 — 18:00 — Online
Nino Scalbi, LisMath, Instituto Superior Técnico, Universidade de Lisboa
An Introduction to Gerbes
Gerbes being generalisations of bundles over a manifold can be regarded as a geometric realisation of three dimensional cohomology classes of a manifold. Considering the example of circle bundles on a manifold $M$, we recall that such bundles can be described from different perspectives as either
- certain locally free sheaves on $M$
- cocycles $g_{\alpha \beta} : U_{\alpha} \cap U_{\beta} \rightarrow U(1)$ associated to an open cover $\{ U_{\alpha} \}$ of $M$
- principal $U(1)$ bundles over $M$
In a similar fashion also gerbes allow such characterizations, generalising the same ideas. This talk will focus mostly on the different definitions of gerbes and their applications in field theory.
Bibliography:
[1] M. K. Murray, An introduction to bundle gerbes, arXiv:0712.1651.
[2] G. Segal, Topological structures in string theory, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 359, number 1784, pp. 1389–1398, 2001, The Royal Society.
[3] J.-L. Brylinski, Loop Spaces, Characteristic Classes and Geometric Quantization, 2007, Springer Science & Business Media.
[4] J. Fuchs, T. Nikolaus, C. Schweigert and K. Waldorf, Bundle gerbes and surface holonomy, arXiv:0901.2085.
See also
An Introduction to Gerbes.pdf
