A gauge-field approach to 3- and 4-manifold invariants

Bogusław Broda

Banach Center Publications (1997)

  • Volume: 39, Issue: 1, page 201-209
  • ISSN: 0137-6934

Abstract

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An approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry is presented.

How to cite

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Broda, Bogusław. "A gauge-field approach to 3- and 4-manifold invariants." Banach Center Publications 39.1 (1997): 201-209. <http://eudml.org/doc/208663>.

@article{Broda1997,
abstract = {An approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry is presented.},
author = {Broda, Bogusław},
journal = {Banach Center Publications},
keywords = {topological invariants; Reshetikhin-Turaev-Witten; manifolds; Chern-Simons gauge theory; gauge symmetry},
language = {eng},
number = {1},
pages = {201-209},
title = {A gauge-field approach to 3- and 4-manifold invariants},
url = {http://eudml.org/doc/208663},
volume = {39},
year = {1997},
}

TY - JOUR
AU - Broda, Bogusław
TI - A gauge-field approach to 3- and 4-manifold invariants
JO - Banach Center Publications
PY - 1997
VL - 39
IS - 1
SP - 201
EP - 209
AB - An approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry is presented.
LA - eng
KW - topological invariants; Reshetikhin-Turaev-Witten; manifolds; Chern-Simons gauge theory; gauge symmetry
UR - http://eudml.org/doc/208663
ER -

References

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  1. [Bro1] B. Broda, A surgical invariant of 4-manifolds, Proc. Conf. on Quantum Topology, Kansas 1993, D. N. Yetter (ed.), World Scientific, Singapore, 1994, 45-50. 
  2. [Bro2] B. Broda, TQFT versus RCFT: 3-D topological invariants, Modern Phys. Lett. A 10 (1995), 331-336. Zbl1020.57501
  3. [Bro3] B. Broda, Chern-Simons approach to three-manifold invariants, Modern Phys. Lett. A 10 (1995), 487-493. Zbl1020.57502
  4. [CdS] E. César de Sá, A link calculus for 4-manifolds, Topology of low-dimensional manifolds, Proc. Sec. Conf. Sussex, Lecture Notes in Math. 722, Springer, Berlin, 1979, 16-30. 
  5. [CKY1] L. Crane, L. H. Kauffman and D. Yetter, U q ( s l 2 ) Invariants at Principal and Non-principal Roots of Unity, Adv. Appl. Clifford Algebras 3 (1993), 223. 
  6. [CKY2] L. Crane, L. H. Kauffman and D. Yetter, On the Classicality of Broda's SU(2) Invariants of 4-Manifolds, Adv. Appl. Clifford Algebras 3 (1993), 223. Zbl0856.57014
  7. [CY] L. Crane and D. Yetter, A categorical construction of 4d topological quantum field theories, Quantum Topology, L. Kauffman and R. Baadhio (eds.), World Scientific, Singapore, 1993. Zbl0841.57030
  8. [Oht] T. Ohtsuki, A polynomial invariant of integral homology 3-spheres, Math. Proc. Cambridge Philos. Soc. 117 (1995), 83-112. Zbl0843.57019
  9. [RT] N. Reshetikhin and V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547-597. Zbl0725.57007
  10. [Rol] D. Rolfsen, Knots and Links, Publish or Perish, Wilmington, 1976, Chapt. 9. 
  11. [TV] V. G. Turaev and O. Y. Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology 31 (1992), 865-902. Zbl0779.57009
  12. [Wit1] E. Witten, Quantum Field Theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. Zbl0667.57005
  13. [Wit2] E. Witten, Monopoles and four-manifolds, Math. Res. Lett. 1 (1994), 769-796. Zbl0867.57029

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