5 papers
Extension of algebroids Part I: The Construction
Simon-Raphael Fischer
In this series of two papers we will generalise the concept of extending a Lie algebroid by a Lie algebra bundle, leading to a notion of extending a Lie algebroid by another Lie al…
Topological Classification of Symmetry Breaking and Vacuum Degeneracy
Simon-Raphael Fischer, Mehran Jalali Farahani, Hyungrok Kim +1
We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneou…
A classification of neighborhoods around leaves of a singular foliation
Simon-Raphael Fischer, Camille Laurent-Gengoux
We classify singular foliations admitting a given leaf and a given transverse singular foliation.
Adjusted Connections I: Differential Cocycles for Principal Groupoid Bundles with Connection
Simon-Raphael Fischer, Mehran Jalali Farahani, Hyungrok Kim +1
We develop a new perspective on principal bundles with connection as morphisms from the tangent bundle of the underlying manifold to a classifying dg-Lie groupoid. This groupoid ca…
Integrating curved Yang-Mills gauge theories
Simon-Raphael Fischer
We construct a gauge theory based on principal bundles equipped with a right -action, where is a Lie group bundle instead of a Lie group. D…