# 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

The prequantum line bundle on the moduli space of flat SU(N) connections on a Riemann surface and... 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 $${\mathbb C}P^\infty$$ C P ∞ . Applications to the stable moduli space of flat unitary connections are also discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Letters in Mathematical Physics Springer Journals

# 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

, Volume 107 (9) – Mar 20, 2017
9 pages

/lp/springer_journal/the-prequantum-line-bundle-on-the-moduli-space-of-flat-su-n-ECkeXXwH0r
Publisher
Springer Netherlands
Subject
Physics; Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations
ISSN
0377-9017
eISSN
1573-0530
D.O.I.
10.1007/s11005-017-0956-9
Publisher site
See Article on Publisher Site

### Abstract

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 $${\mathbb C}P^\infty$$ C P ∞ . Applications to the stable moduli space of flat unitary connections are also discussed.

### Journal

Letters in Mathematical PhysicsSpringer Journals

Published: Mar 20, 2017

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