On universal relations in Gauge theory

Author:
Selman Akbulut

Journal:
Trans. Amer. Math. Soc. **348** (1996), 1329-1355

MSC (1991):
Primary 57R19; Secondary 58D27

DOI:
https://doi.org/10.1090/S0002-9947-96-01394-3

MathSciNet review:
1307997

Full-text PDF

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. 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**

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:
https://doi.org/10.1090/S0002-9947-96-01394-3

Received by editor(s):
November 1, 1994

Additional Notes:
Partially supported by the N.S.F

Article copyright:
© Copyright 1996
American Mathematical Society