Geometric string structures on homogeneous spaces

This post is just to provide a link to slides for a talk of the above title, for a Zoom talk held in the UNAM categories seminar.

Abstract: The notion of string structure on a space X goes back to work in the 1980s, particularly of Killingback, starting as an analogue of a spin structure on the loop space LX. In the decades since, increasingly refined versions of string structures have been defined. Ultimately, one wants to have a full-fledged String 2-bundle with connection, a structure from higher geometry, which combines differential geometry and category-theoretic structures. A half-way step, due to Waldorf, is known as a “geometric string structure”. Giving examples of such structures, despite existence being know, has been an outstanding problem for some time. In this talk, I will describe joint work with Raymond Vozzo on our framework for working with the structure that obstruct the existence of a geometric string structure, which is a 2-gerbe with connection, as well as give a general construction of geometric string structures on reductive homogeneous spaces.

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