On the Burns-Epstein invariants of spherical CR 3-manifolds
Annales de l'Institut Fourier, Volume 61 (2011) no. 2, pp. 775-797.

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.

Dans cet article nous développons une méthode pour calculer l’invariant de Burns-Epstein d’une sphère d’homologie CR sphérique, à un nombre entier près, de sa représentation d’holonomie. Comme application, nous donnons une formule pour l’invariant de Burns-Epstein, modulo un nombre entier, d’une structure CR sphérique sur une sphère d’homologie fibrée de Seifert en termes de sa représentation d’holonomie.

DOI: 10.5802/aif.2629
Classification: 32V05, 58J28, 32Q20
Keywords: Spherical CR structures, Burns-Epstein invariant, Chern-Simons invariant
Mot clés : structures CR sphériques, invariant de Burns-Epstein, invariant de Chern-Simons

Vu, Khoi The 1

1 Institute of Mathematics 18 Hoang Quoc Viet road, 10307 Hanoi (Vietnam)
@article{AIF_2011__61_2_775_0,
     author = {Vu, Khoi The},
     title = {On the {Burns-Epstein} invariants of  spherical {CR} 3-manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {775--797},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {61},
     number = {2},
     year = {2011},
     doi = {10.5802/aif.2629},
     mrnumber = {2895073},
     zbl = {1228.32036},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2629/}
}
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
SP  - 775
EP  - 797
VL  - 61
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2629/
DO  - 10.5802/aif.2629
LA  - en
ID  - AIF_2011__61_2_775_0
ER  - 
%0 Journal Article
%A Vu, Khoi The
%T On the Burns-Epstein invariants of  spherical CR 3-manifolds
%J Annales de l'Institut Fourier
%D 2011
%P 775-797
%V 61
%N 2
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.2629/
%R 10.5802/aif.2629
%G en
%F AIF_2011__61_2_775_0
Vu, Khoi The. On the Burns-Epstein invariants of  spherical CR 3-manifolds. Annales de l'Institut Fourier, Volume 61 (2011) no. 2, pp. 775-797. doi : 10.5802/aif.2629. https://aif.centre-mersenne.org/articles/10.5802/aif.2629/

[1] Biquard, Olivier; Herzlich, Marc A Burns-Epstein invariant for ACHE 4-manifolds, Duke Math. J., Volume 126 (2005) no. 1, pp. 53-100 | DOI | MR | Zbl

[2] Biquard, Olivier; Herzlich, Marc; Rumin, Michel Diabatic limit, eta invariants and Cauchy-Riemann manifolds of dimension 3, Ann. Sci. École Norm. Sup. (4), Volume 40 (2007) no. 4, pp. 589-631 | DOI | Numdam | MR | Zbl

[3] Burns, D.; Epstein, C. L. A global invariant for three-dimensional CR-manifolds, Invent. Math., Volume 92 (1988) no. 2, pp. 333-348 | DOI | MR | Zbl

[4] Burns, D.; Epstein, C. L. Characteristic numbers of bounded domains, Acta Math., Volume 164 (1990) no. 1-2, pp. 29-71 | DOI | MR | Zbl

[5] Chen, S. S.; Greenberg, L. Hyperbolic spaces, Contributions to analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 49-87 | MR | Zbl

[6] Chêng, Jih Hsin; Lee, John M. The Burns-Epstein invariant and deformation of CR structures, Duke Math. J., Volume 60 (1990) no. 1, pp. 221-254 | DOI | MR | Zbl

[7] Chern, Shiing Shen; Simons, James Characteristic forms and geometric invariants, Ann. of Math. (2), Volume 99 (1974), pp. 48-69 | DOI | MR | Zbl

[8] Falbel, Elisha; Gusevskii, Nikolay Spherical CR-manifolds of dimension 3, Bol. Soc. Brasil. Mat. (N.S.), Volume 25 (1994) no. 1, pp. 31-56 | DOI | MR | Zbl

[9] Freed, Daniel S. Classical Chern-Simons theory. I, Adv. Math., Volume 113 (1995) no. 2, pp. 237-303 | DOI | MR | Zbl

[10] Hansen, Mogens Lemvig Weak amenability of the universal covering group of SU (1,n), Math. Ann., Volume 288 (1990) no. 3, pp. 445-472 | DOI | EuDML | MR | Zbl

[11] Jacobowitz, Howard An introduction to CR structures, Mathematical Surveys and Monographs, 32, American Mathematical Society, Providence, RI, 1990 | MR | Zbl

[12] Kamishima, Yoshinobu; Tsuboi, Takashi CR-structures on Seifert manifolds, Invent. Math., Volume 104 (1991) no. 1, pp. 149-163 | DOI | EuDML | MR | Zbl

[13] Khoi, Vu The A cut-and-paste method for computing the Seifert volumes, Math. Ann., Volume 326 (2003) no. 4, pp. 759-801 | DOI | MR | Zbl

[14] Khoi, Vu The On the SU (2,1) representation space of the Brieskorn homology spheres, J. Math. Sci. Univ. Tokyo, Volume 14 (2007) no. 4, pp. 499-510 | MR | Zbl

[15] Kirk, Paul; Klassen, Eric Chern-Simons invariants of 3-manifolds and representation spaces of knot groups, Math. Ann., Volume 287 (1990) no. 2, pp. 343-367 | DOI | EuDML | MR | Zbl

[16] Kirk, Paul; Klassen, Eric Chern-Simons invariants of 3-manifolds decomposed along tori and the circle bundle over the representation space of T 2 , Comm. Math. Phys., Volume 153 (1993) no. 3, pp. 521-557 http://projecteuclid.org/getRecord?id=euclid.cmp/1104252787 | DOI | MR | Zbl

[17] Nishi, Haruko SU (n)-Chern-Simons invariants of Seifert fibered 3-manifolds, Internat. J. Math., Volume 9 (1998) no. 3, pp. 295-330 | DOI | MR | Zbl

Cited by Sources: