Topological quantum field theory

Michael F. Atiyah

Publications Mathématiques de l'IHÉS (1988)

  • Volume: 68, page 175-186
  • ISSN: 0073-8301

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Atiyah, Michael F.. "Topological quantum field theory." Publications Mathématiques de l'IHÉS 68 (1988): 175-186. <http://eudml.org/doc/104037>.

@article{Atiyah1988,
author = {Atiyah, Michael F.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {topological quantum field theories; Floer/Gromov theory; holomorphic conformal field theories; Jones/Witten theory; Casson theory; Johnson theory; Thursten theory; Floer/Donaldson theory},
language = {eng},
pages = {175-186},
publisher = {Institut des Hautes Études Scientifiques},
title = {Topological quantum field theory},
url = {http://eudml.org/doc/104037},
volume = {68},
year = {1988},
}

TY - JOUR
AU - Atiyah, Michael F.
TI - Topological quantum field theory
JO - Publications Mathématiques de l'IHÉS
PY - 1988
PB - Institut des Hautes Études Scientifiques
VL - 68
SP - 175
EP - 186
LA - eng
KW - topological quantum field theories; Floer/Gromov theory; holomorphic conformal field theories; Jones/Witten theory; Casson theory; Johnson theory; Thursten theory; Floer/Donaldson theory
UR - http://eudml.org/doc/104037
ER -

References

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  1. [1] M. F. ATIYAH, New invariants of three and four dimensional manifolds, in The Mathematical Heritage of Herman Weyl, Proc. Symp. Pure Math., 48, American Math. Soc. (1988), 285-299. Zbl0667.57018MR89m:57034
  2. [2] S. K. DONALDSON, Polynomial invariants for smooth four-manifolds, to appear in Topology. Zbl0715.57007
  3. [3] A. FLOER, Morse theory for fixed points of symplectic diffeomorphisms, Bull. A.M.S., 16 (1987), 279-281. Zbl0617.53042MR88b:58024
  4. [4] A. FLOER, An instanton invariant for three manifolds, Courant Institute preprint, to appear. Zbl0684.53027
  5. [5] M. GROMOV, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347. Zbl0592.53025MR87j:53053
  6. [6] N. J. HITCHIN, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3), 55 (1987), 59-126. Zbl0634.53045MR89a:32021
  7. [7] D. JOHNSON, A geometric form of Casson's invariant and its connection with Reidemeister torsion, unpublished lecture notes. 
  8. [8] V. F. R. JONES, Hecke algebra representations of braid groups and link polynomials, Ann. of Math., 126 (1987), 335-388. Zbl0631.57005MR89c:46092
  9. [9] A. PRESSLEY and G. B. SEGAL, Loop Groups, Oxford University Press (1988). Zbl0638.22009
  10. [10] G. B. SEGAL, The definition of conformal field theory (to appear). Zbl0657.53060
  11. [11] E. WITTEN, Super-symmetry and Morse theory, J. Diff. Geom., 17 (4) (1982), 661-692. Zbl0499.53056MR84b:58111
  12. [12] E. WITTEN, Quantum field theory and the Jones polynomial, Comm. Math. Phys. (to appear). Zbl0667.57005
  13. [13] E. WITTEN, Topological quantum field theory, Comm. Math. Phys., 117 (1988), 353-386. Zbl0656.53078MR89m:57037
  14. [14] E. WITTEN, Topological sigma models, Comm. Math. Phys., 118 (1988), 411-449. Zbl0674.58047MR90b:81080
  15. [15] E. WITTEN, 2 + 1 dimensional gravity as an exactly soluble system, Nucl. Phys. B, 311 (1988/1989), 46-78. Zbl1258.83032MR90a:83041
  16. [16] E. WITTEN, Topology changing amplitudes in 2 + 1 dimensional gravity, Nucl. Phys. B (to appear). 
  17. [17] E. WITTEN, Elliptic genera and quantum field theory, Comm. Math. Phys., 109 (1987), 525-536. Zbl0625.57008MR89i:57017

Citations in EuDML Documents

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  1. Michael Atiyah, The Jones-Witten invariants of knots
  2. V. Poénaru, C. Tanasi, A note on the wick of the Casson handles
  3. Florin Dumitrescu, Another Look at Connections
  4. Vladimir G. Turaev, Axioms for topological quantum field theories
  5. A. A. Balinsky, Racks and orbits of dressing transformations
  6. David N. Pham, 𝔤 -quasi-Frobenius Lie algebras
  7. Sylvain Gervais, The p 1 -central extension of the Mapping Class Group of orientable surfaces
  8. Vladimir Turaev, Quantum invariants of links and 3-valent graphs in 3-manifolds
  9. Patrick Gilmer, A TQFT for Wormhole cobordisms over the field of rational functions
  10. R. J. Lawrence, Asymptotic Expansions of Witten-Reshetikhin-Turaev Invariants for Some Simple 3 -Manifolds

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