The prequantum line bundle on the moduli space of flat SU(N) connections on a Riemann surface and the homotopy of the large N limit

We show that the prequantum line bundle on the moduli space of flat SU (2) connections on a closed Riemann surface of positive genus has degree 1. It then follows from work of Lawton and the second author that the classifying map for this line bundle induces a homotopy equivalence between the stable...

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Bibliographic Details
Published in:Letters in mathematical physics 2017-09, Vol.107 (9), p.1581-1589
Main Authors: Jeffrey, Lisa C., Ramras, Daniel A., Weitsman, Jonathan
Format: Article
Language:English
Subjects:
Bundling
Complex Systems
Geometry
Group Theory and Generalizations
Infinity
Linear algebra
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum theory
Theoretical
Topological manifolds
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Summary:We show that the prequantum line bundle on the moduli space of flat SU (2) connections on a closed Riemann surface of positive genus has degree 1. It then follows from work of Lawton and the second author that the classifying map for this line bundle induces a homotopy equivalence between the stable moduli space of flat SU ( n ) connections, in the limit as n tends to infinity, and C P ∞ . Applications to the stable moduli space of flat unitary connections are also discussed.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-017-0956-9