Pushforwards and Gauge Transformations for Categorical Connections
Saikat Chatterjee, Amitabha Lahiri, and Ambar N. Sengupta
TL;DR
This paper develops a framework for pushforwards of categorical connections on principal bundles, revealing a new transformation that merges gauge transformations with affine translations in decorated path spaces.
Contribution
It introduces a novel construction of pushforwards for categorical connections and applies it to decorated path spaces, unifying gauge transformations with affine translations.
Findings
Established a method for pushforwards of categorical connections.
Derived a combined gauge and affine translation transformation.
Applied the theory to decorated path spaces in principal bundles.
Abstract
We construct and study pushforwards of categorical connections on categorical principal bundles. Applying this construction to the case of decorated path spaces in principal bundles, we obtain a transformation of classical connections that combines the traditional gauge transformation with an affine translation.
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Taxonomy
TopicsSpatial Cognition and Navigation · Homotopy and Cohomology in Algebraic Topology · Mathematics Education and Teaching Techniques