0035-001X 0035-001X S0035-001X2007001000029 México 00 08 2007 00 08 2007 53 150 154

Donaldson–Witten invariants for flows on four manifolds

 

R. Santos–Silva

 

Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, P.O. Box 14–740, 07000 México D.F., México, e–mail: rsantos@fis.cinvestav.mx

 

Recibido el 1 de mayo de 2006
Aceptado el 1 de noviembre de 2006

 

Abstract

]]> After a survey of the cohomological quantum field theory, we review the computation of their Donaldson–Witten invariants. These invariants are generalized for smooth flows defined on the four manifold using notion of asymptotic cycles of higher dimensions than one introduced recently by S. Schwartzman.

Keywords: Topological field theory; supersymmetric Yang–Mills; topological invariants; dynamical Systems.

 

Resumen

Después de repasar la teoría co–homológica de campos, revisamos los cálculos de los invariantes de Donaldson–Witten. Estos invariantes son generalizados para flujos suaves definidos en cuatro variedades usando la noción de ciclos asintóticos para dimensiones mayores que uno introducido recientemente por S. Schwartzman.

Descriptores: Teoría topológica de campos; Yang–Mills supersimétrico; invariantes topológicos; sistemas dinámicos

 

PACS: 11.10.–z; 11.15.–q; 10.30.Pb; 02.40.–k

 

DESCARGAR ARTÍCULO EN FORMATO PDF

]]>  

Acknowledgments

I am indebted with Hugo García–Compeán for his comments and to CINVESTAV campus Monterrey for the hospitality and support. This review was supported by CONACyT graduate fellowship.

 

References

1. E. Witten, Commun. Math. Phys. 121 (1989) 351.                                     [ Links ]

2. A. Verjovsky and R. Vila Freyer, Commun. Math. Phys. 163 (1994) 73.               [ Links ]

3. S. Schwartzman, Ann. Math. 66 (1957) 270.        [ Links ]

4. M. Freedman and F. Quinn, Topology of Four Manifolds, (Princeton University Press, Princeton, 1990) Math. Series No. 39.        [ Links ]

5. S.K. Donaldson and P. Kronheimer, The Geometry of Four Manifolds, (Oxford University Press, Oxford, 1990).        [ Links ]

6. E. Witten, Commun. Math. Phys. 117 (1988) 353.        [ Links ]

 7. E. Witten, Int. J. Mod. Phys. A 6 (1991) 2775.         [ Links ]

8. D.K. Arrowsmith and C.M. Place, An Introduction to Dynamical Systems, (Cambridge University Press, Cambridge 1990).        [ Links ]

9. S. Schwartzman, Canad. J. Math. 55 (2003) 636.         [ Links ]

10. D. Ruelle and D. Sullivan, Topology 14 (1975) 319.        [ Links ]

11. D. Sullivan, Invent. Math. 36 (1976) 225.        [ Links ] ]]> 1989 121 121 351 1994 163 163 73 1957 66 66 270 1990 1990 1988 117 117 353 1991 A 6 A 6 2775 1990 2003 55 55 636 1975 14 14 319 1976 36 36 225