On the Burns-Epstein invariants of spherical CR 3-manifolds

Khoi The Vu[1]

  • [1] Institute of Mathematics 18 Hoang Quoc Viet road, 10307 Hanoi (Vietnam)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 2, page 775-797
  • ISSN: 0373-0956

Abstract

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In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.

How to cite

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Vu, Khoi The. "On the Burns-Epstein invariants of spherical CR 3-manifolds." Annales de l’institut Fourier 61.2 (2011): 775-797. <http://eudml.org/doc/219769>.

@article{Vu2011,
abstract = {In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.},
affiliation = {Institute of Mathematics 18 Hoang Quoc Viet road, 10307 Hanoi (Vietnam)},
author = {Vu, Khoi The},
journal = {Annales de l’institut Fourier},
keywords = {Spherical CR structures; Burns-Epstein invariant; Chern-Simons invariant; spherical CR structures},
language = {eng},
number = {2},
pages = {775-797},
publisher = {Association des Annales de l’institut Fourier},
title = {On the Burns-Epstein invariants of spherical CR 3-manifolds},
url = {http://eudml.org/doc/219769},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Vu, Khoi The
TI - On the Burns-Epstein invariants of spherical CR 3-manifolds
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 2
SP - 775
EP - 797
AB - In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.
LA - eng
KW - Spherical CR structures; Burns-Epstein invariant; Chern-Simons invariant; spherical CR structures
UR - http://eudml.org/doc/219769
ER -

References

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  11. Howard Jacobowitz, An introduction to CR structures, 32 (1990), American Mathematical Society, Providence, RI Zbl0712.32001MR1067341
  12. Yoshinobu Kamishima, Takashi Tsuboi, CR-structures on Seifert manifolds, Invent. Math. 104 (1991), 149-163 Zbl0728.32012MR1094049
  13. Vu The Khoi, A cut-and-paste method for computing the Seifert volumes, Math. Ann. 326 (2003), 759-801 Zbl1035.57008MR2003451
  14. Vu The Khoi, On the SU ( 2 , 1 ) representation space of the Brieskorn homology spheres, J. Math. Sci. Univ. Tokyo 14 (2007), 499-510 Zbl1155.57001MR2395997
  15. Paul Kirk, Eric Klassen, Chern-Simons invariants of 3 -manifolds and representation spaces of knot groups, Math. Ann. 287 (1990), 343-367 Zbl0681.57006MR1054574
  16. Paul Kirk, Eric Klassen, Chern-Simons invariants of 3 -manifolds decomposed along tori and the circle bundle over the representation space of T 2 , Comm. Math. Phys. 153 (1993), 521-557 Zbl0789.57011MR1218931
  17. Haruko Nishi, SU ( n ) -Chern-Simons invariants of Seifert fibered 3 -manifolds, Internat. J. Math. 9 (1998), 295-330 Zbl0911.57010MR1625367

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