Fundamental Groups & Local Systems (an Equivariant Ending)

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In this off-the-cuff video, I give a rambly bird's eye view of the equivalence of categories between local systems and representations of the fundamental group of a sufficiently nice topological space. I also discuss the corresponding story for the equivariant etale fundamental group of a variety.

Introduction (0:00)
Fundamental Groups (1:04)
Local Systems (4:40)
The Main Theorem (9:50)
Getting Etale (20:40)
Equivariance (25:50)

K-Theory

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Nice video! I have been putting off learning the details of this equivalence, so this was useful to help me keep putting it off. By the way, I have just recently learned about the Riemann–Hilbert correspondence between local systems (hence pi_1-representations) and vector bundles with flat connection—is this something you've had to deal with?

jake

Fundamental Groups & Local Systems (an Equivariant Ending)

Fundamental Groups & Local Systems (an Equivariant Ending)

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