NONCOMMUTATIVE PRINCIPAL BUNDLES AND CENTRAL EXTENSIONS

Speaker(s)

STEFAN WAGNER

Affiliation

Blekinge Tekniska Högskola, Karlskrona, Sweden

Language of the talk

English

Date

March 4, 2026, 5:15 p.m.

Information about the event

IMPAN - Room 405 & zoom

Title in Polish

NONCOMMUTATIVE PRINCIPAL BUNDLES AND CENTRAL EXTENSIONS

Seminar

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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