Local Triviality Dimension and Borsuk-Ulam Type Conjectures

Jianchao Wu ⽡  (Penn State University)

14:00-15:00, Jan 2, 2018   Science Building A1510


The classical Borsuk-Ulam theorem may be seen as a statement about the complexity of the n-spheres as principal Z/2Z-bundles. The truthfulness of analogous statements for other principal bundles of compact groups, or even compact quantum groups, were proposed by Baum, Dabrowski, and Hajac. For classical principal bundles, a dimensional notion called G-index appears to play a crucial role in this quest. I will talk about recent joint work with Eusebio Gardella, Piotr Hajac, and Mariusz Tobolski, where we introduce the local triviality dimension, a generalization of G-index for noncommutative principal bundles. It is inspired by the Rokhlin dimension and can be used to extend Borsuk-Ulam-type results to the noncommutative setting.

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