The p 1 -central extension of the Mapping Class Group of orientable surfaces

Sylvain Gervais

Banach Center Publications (1998)

  • Volume: 42, Issue: 1, page 111-117
  • ISSN: 0137-6934

Abstract

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Topological Quantum Field Theories are closely related to representations of Mapping Class Groups of surfaces. Considering the case of the TQFTs derived from the Kauffman bracket, we describe the central extension coming from this representation, which is just a projective extension.

How to cite

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Gervais, Sylvain. "The $p_1$-central extension of the Mapping Class Group of orientable surfaces." Banach Center Publications 42.1 (1998): 111-117. <http://eudml.org/doc/208798>.

@article{Gervais1998,
abstract = {Topological Quantum Field Theories are closely related to representations of Mapping Class Groups of surfaces. Considering the case of the TQFTs derived from the Kauffman bracket, we describe the central extension coming from this representation, which is just a projective extension.},
author = {Gervais, Sylvain},
journal = {Banach Center Publications},
keywords = {mapping class group; TQFT; -structure},
language = {eng},
number = {1},
pages = {111-117},
title = {The $p_1$-central extension of the Mapping Class Group of orientable surfaces},
url = {http://eudml.org/doc/208798},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Gervais, Sylvain
TI - The $p_1$-central extension of the Mapping Class Group of orientable surfaces
JO - Banach Center Publications
PY - 1998
VL - 42
IS - 1
SP - 111
EP - 117
AB - Topological Quantum Field Theories are closely related to representations of Mapping Class Groups of surfaces. Considering the case of the TQFTs derived from the Kauffman bracket, we describe the central extension coming from this representation, which is just a projective extension.
LA - eng
KW - mapping class group; TQFT; -structure
UR - http://eudml.org/doc/208798
ER -

References

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  1. [A1] M. Atiyah, Topological quantum field theories, Publ. Math. IHES 68 (1989), 175-186 . Zbl0692.53053
  2. [A2] M. Atiyah, On framings of 3-manifolds, Topology 29 (1990), 1-7. Zbl0716.57011
  3. [BHMV1] C. Blanchet, N. Habegger, G. Masbaum and P. Vogel, Three-manifold invariants derived from the Kauffman bracket, Topology 31 (1992), 685-699. Zbl0771.57004
  4. [BHMV2] C. Blanchet, N. Habegger, G. Masbaum and P. Vogel, Remarks on the Three-manifold Invariants θ p , in ’Operator Algebras, Mathematical Physics, and Low Dimensional Topology’ (NATO Workshop July 1991) Edited by R. Herman and B. Tanbay, Research Notes in Mathematics Vol 5, 39-59. 
  5. [BHMV3] C. Blanchet, N. Habegger, G. Masbaum and P. Vogel, Topological Quantum Field Theories derived from the Kauffman bracket, Topology 34 (1995), 883-927. Zbl0887.57009
  6. [G1] S. Gervais, Etude de certaines extensions centrales du 'mapping class group' des surfaces orientables, thèse, Université de Nantes, 1994. 
  7. [G2] S. Gervais, Presentation and central extensions of Mapping Class Groups, Trans. of Amer. Math. Soc. 348 (1996), 3097-3132. Zbl0861.57023
  8. [M-R] G. Masbaum and J. Roberts, On Central Extensions of Mapping Class Groups, Math. Ann. 302 (1995), 131-150. Zbl0823.57010
  9. [St] N. Steenrod, The topology of fibre bundles, Princeton University Press, 1951. Zbl0054.07103
  10. [W] B. Wajnryb, A simple presentation for the Mapping Class Group of an orientable surface, Israel Journal of Math. 45 (1983), 157-174 . Zbl0533.57002

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