Equivariant principal infinity-bundles
Hisham Sati, Urs Schreiber

TL;DR
This paper develops a unified classification framework for equivariant principal infinity-bundles with truncated structure groups, using advanced homotopy theory and embedding techniques, extending classical results and applications in topological phases and string theory.
Contribution
It introduces a new classification approach for equivariant principal bundles via singular-cohesive homotopy theory, generalizing classical results and incorporating non-classical structure groups.
Findings
Unified classification results for equivariant principal bundles with truncated groups
Extension of classical classification to non-compact and infinite groups
Application to twists in equivariant K-theory and topological phases
Abstract
In this book we prove unified classification results for equivariant principal bundles when the topological structure group is truncated. The conceptually transparent proof invokes a smooth Oka principle, which becomes available after faithfully embedding traditional equivariant topology into the singular-cohesive homotopy theory of globally equivariant higher smooth stacks. This works for discrete equivariance groups acting properly on smooth manifolds with resolvable singularities, whence we are equivalently describing principal bundles on good orbifolds. In preparation, we re-develop the theory of equivariant principal bundles from scratch by systematic use of Grothendieck's internalization method. In particular we prove that all equivariant local triviality conditions considered in the literature are implied by regarding G-equivariant principal bundles as principal bundles…
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Black Holes and Theoretical Physics
