NONCOMMUTATIVE PRINCIPAL BUNDLES AND CENTRAL EXTENSIONS

Prelegent(ci)

STEFAN WAGNER

Afiliacja

Blekinge Tekniska Högskola, Karlskrona, Sweden

Język referatu

angielski

Termin

4 marca 2026 17:15

Informacje na temat wydarzenia

IMPAN - Room 405 & zoom

Tytuł w języku polskim

NONCOMMUTATIVE PRINCIPAL BUNDLES AND CENTRAL EXTENSIONS

Seminarium

North Atlantic Noncommutative Geometry Seminar

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In Riemannian geometry, spin structures arise from lifting frame bundles along the universal covering of the structure group, with the existence and classification governed by cohomological obstructions. In this talk, I will present a noncommutative analogue of this lifting problem. I will explain how the lifting of free C*-dynamical systems (natural models for noncommutative principal bundles) along central extensions of the structure group can be formulated and solved in a systematic way. Using factor system techniques and equivariant Picard theory, we obtain precise existence criteria and a complete classification of such liftings in terms of cohomological invariants. This framework unifies geometric, cohomological, and operator-algebraic perspectives. It also recovers the classical theory of spin structures as a special case and applies to a range of concrete noncommutative examples.

 

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