On the Derivative of 2-Holonomy for a Non-Abelian Gerbe

Author

Cheyne J. Miller, The Graduate Center, City University of New YorkFollow

Date of Degree

9-2016

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Thomas Tradler

Committee Members

John Terilla

Thomas Tradler

Scott Wilson

Subject Categories

Algebra | Geometry and Topology

Keywords

Gerbes, Hochschild Complex, Holonomy, Parallel Transport, non abelian, cohomology

Abstract

The local 2-holonomy for a non abelian gerbe with connection is first studied via a local zig-zag Hochschild complex. Next, by locally integrating the cocycle data for our gerbe with connection, and then glueing this data together, an explicit definition is offered for a global version of 2-holonomy. After showing this definition satisfies the desired properties for 2-holonomy, its derivative is calculated whereby the only interior information added is the integration of the 3-curvature. Finally, for the case when the surface being mapped into the manifold is a sphere, the derivative of 2-holonomy is extended to an equivariant closed form in the spirit of the construction of Tradler-Wilson-Zeinalian for abelian gerbes.

Recommended Citation

Miller, Cheyne J., "On the Derivative of 2-Holonomy for a Non-Abelian Gerbe" (2016). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/1583