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The Dijkgraaf–Witten Invariants of Circle Bundles

Abstract

Turaev (J. Geom. Phys. 57: 2419–2430, 2007) proves a formula for the Dijkgraaf–Witten invariants of surfaces in terms of projective representations by using the state sum invariant technique from quantum topology. In Khoi (J. Knot Theory Ramif. 20: 837–846, 2011), the author gives another proof of Turaev’s theorem by using classical method of characters and representation theory. The purpose of this paper is to prove a formula for the Dijkgraaf–Witten invariants of a circle bundle over a surface by using techniques from Khoi (J. Knot Theory Ramif. 20: 837–846, 2011).

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References

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Acknowledgments

The author would like to thank the VAST-JSPS joint project for the travel support to attend the conference to report on the result of this paper. The author would like to express his gratitude to the Vietnam Institute for Advanced Study in Mathematics for the support during the revision of the paper. We thank the anonymous referees for the careful reading of our manuscript and the valuable comments.

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Correspondence to Vu The Khoi.

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Dedicated to Professor Mutsuo Oka on the occasion of his 65th birthday

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2011.46.

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Khoi, V.T. The Dijkgraaf–Witten Invariants of Circle Bundles. Vietnam J. Math. 42, 393–399 (2014). https://doi.org/10.1007/s10013-014-0087-x

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  • DOI: https://doi.org/10.1007/s10013-014-0087-x

Keywords

  • Dijkgraaf–Witten invariants
  • Circle bundles

Mathematics Subject Classification (2000)

  • Primary 57M27
  • Secondary 57R56