|
On universal relations in Gauge theory
Author:
Selman Akbulut
Journal:
Trans. Amer. Math. Soc. 348 (1996), 1329-1355
MSC (1991):
Primary 57R19; Secondary 58D27
MathSciNet review:
1307997
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this paper we study the algebraic topology of gauge group, and as a corollary we deduce some universal relations among Donaldson polynomials of smooth 4-manifolds.
- [A]
S. Akbulut, Torsion in gauge theory, Turkish Math. 19 (1995), 167--177.
- [AMR]
S. Akbulut, T. Mrowka and Y. Ruan, Torsion classes and a universal constraint on Donaldson invariants for odd manifolds, Trans. Amer. Math. Soc. 347 (1995), 63--76. CMP 95:02
- [AS]
M.
F. Atiyah and I.
M. Singer, The index of elliptic operators. IV, Ann. of Math.
(2) 93 (1971), 119–138. MR 0279833
(43 #5554)
- [D]
S.
K. Donaldson, Connections, cohomology and the intersection forms of
4-manifolds, J. Differential Geom. 24 (1986),
no. 3, 275–341. MR 868974
(88g:57033)
- [DK]
S.
K. Donaldson and P.
B. Kronheimer, The geometry of four-manifolds, Oxford
Mathematical Monographs, The Clarendon Press Oxford University Press, New
York, 1990. Oxford Science Publications. MR 1079726
(92a:57036)
- [DW]
A.
Dold and H.
Whitney, Classification of oriented sphere bundles over a
4-complex, Ann. of Math. (2) 69 (1959),
667–677. MR 0123331
(23 #A659)
- [FS]
Ronald
Fintushel and Ronald
J. Stern, 2-torsion instanton
invariants, J. Amer. Math. Soc.
6 (1993), no. 2,
299–339. MR 1168958
(93f:57038), http://dx.doi.org/10.1090/S0894-0347-1993-1168958-8
- [FM]
R. Friedman and J. Morgan, Smooth four manifolds and complex surfaces, A series of Modern Surveys in Mathematics no. 27, Springer-Verlag, 1995.
- [J]
I.
M. James, The topology of Stiefel manifolds, Cambridge
University Press, Cambridge, 1976. London Mathematical Society Lecture Note
Series, No. 24. MR 0431239
(55 #4240)
- [M]
Gregor
Masbaum, On the cohomology of the classifying space of the gauge
group over some 4-complexes, Bull. Soc. Math. France
119 (1991), no. 1, 1–31 (English, with French
summary). MR
1101938 (92a:55009)
- [Mo]
Kai-Cheong
Mong, Some polynomials on the blow-up of
𝑃₂(𝐶), J. Reine Angew. Math.
419 (1991), 67–78. MR 1116918
(92i:14042), http://dx.doi.org/10.1515/crll.1991.419.67
- [MT]
Robert
E. Mosher and Martin
C. Tangora, Cohomology operations and applications in homotopy
theory, Harper & Row Publishers, New York, 1968. MR 0226634
(37 #2223)
- [T]
Emery
Thomas, Seminar on fiber spaces, Lectures delivered in 1964 in
Berkeley and 1965 in Zürich. Berkeley notes by J. F. McClendon.
Lecture Notes in Mathematics, vol. 13, Springer-Verlag, Berlin, 1966.
MR
0203733 (34 #3582)
- [To]
Hirosi
Toda, Composition methods in homotopy groups of spheres,
Annals of Mathematics Studies, No. 49, Princeton University Press,
Princeton, N.J., 1962. MR 0143217
(26 #777)
- [A]
- S. Akbulut, Torsion in gauge theory, Turkish Math. 19 (1995), 167--177.
- [AMR]
- S. Akbulut, T. Mrowka and Y. Ruan, Torsion classes and a universal constraint on Donaldson invariants for odd manifolds, Trans. Amer. Math. Soc. 347 (1995), 63--76. CMP 95:02
- [AS]
- M. Atiyah and I.M. Singer, The index of elliptic operators IV, Ann. of Math. (2) 93 (1971), 119--138. MR 43:5554
- [D]
- S. Donaldson, Connections, cohomology and the intersection of four manifolds, J. Differential Geometry 24 (1986), 275--341.MR 88g:57033
- [DK]
- S.K. Donaldson and P. Kronheimer, The geometry of 4-manifolds, Oxford Math. Monographs, Oxford Univ. Press, 1990.MR 92a:57036
- [DW]
- H. Whitney and A. Dold, Classification of oriented sphere bundle over a 4-complex, Ann. of Math. 69 (1959), 667--677.MR 23:A659
- [FS]
- R. Fintushel and R. Stern,
 -torsion instanton invariants, J. Amer. Math. Soc. 6 (1993), 299--339.MR 93f:57038
- [FM]
- R. Friedman and J. Morgan, Smooth four manifolds and complex surfaces, A series of Modern Surveys in Mathematics no. 27, Springer-Verlag, 1995.
- [J]
- I.M. James, The topology of Steifel manifolds, London Math Soc. Lecture Notes, no. 24, Cambridge Univ. Press, 1976. MR 55:4240
- [M]
- G. Masbaum, On the cohomology of the classifying space of the gauge group over some
 -complexes, Bull. Soc. France 119 (1991), 1--31.MR 92a:55009
- [Mo]
- K-C. Mong, Some polynomials on the blow-up of
 , J. Reine Angew. Math. 419 (1991), 67--78. MR 92i:14042
- [MT]
- R.E. Moser and M.C. Tangora, Cohomology operations and applications in homotopy theory, Harper and Row, 1968.MR 37:2223
- [T]
- E. Thomas, Seminar on fiber spaces, Lecture Notes in Math., vol. 13, Springer-Verlag, 1966.MR 34:3582
- [To]
- H. Toda, Composition methods in homotopy groups of spheres, Ann. of Math Stud., no. 49, Princeton Univ. Press, 1962. MR 26:777
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC (1991):
57R19,
58D27
Retrieve articles in all journals
with MSC (1991):
57R19,
58D27
Additional Information
Selman Akbulut
Email:
akbulut@math.msu.edu
DOI:
http://dx.doi.org/10.1090/S0002-9947-96-01394-3
PII:
S 0002-9947(96)01394-3
Received by editor(s):
November 1, 1994
Additional Notes:
Partially supported by the N.S.F
Article copyright:
© Copyright 1996 American Mathematical Society
|
