LisMath Seminar 

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