Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T13:53:12.475Z Has data issue: false hasContentIssue false
  • English
  • Français

On the signature and Euler characteristic of certain four-manifolds

Published online by Cambridge University Press:  24 October 2008

F. E. A. Johnson  and
D. Kotschick†
F. E. A. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
D. Kotschick†
Affiliation:
Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland
Get access Rights & Permissions [Opens in a new window]

Extract

Let M be a smooth closed connected oriented 4-manifold; we shall say that M satisfies Winkelnkemper's inequality when its signature, σ(M), and Euler characteristic, X(M), are related by

This inequality is trivially true for manifolds M with first Betti number b1(M) ≤ 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 3 , November 1993 , pp. 431 - 437
Copyright
Copyright © Cambridge Philosophical Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Atiyah, M. F.. The signature of fibre bundles. In Collected papers in honour of K. Kodaira (Tokyo University Press, 1969).Google Scholar
[2]Gromov, M.. Volume and bounded cohomology. Publ. Math. IHES 56 (1982), 5–99.Google Scholar
[3]Hitchin, N. J.. Compact four-dimensional Einstein manifolds. J. Differential Geometry 9 (1974), 435–441.CrossRefGoogle Scholar
[4]Kahzdan, D. A.. On the connection between the dual space of a group and the structure of its closed subgroups. Fund. Anal. Appl. (1967), 63–65.CrossRefGoogle Scholar
[5]Kodaira, K.. A certain type of irregular algebraic surface. J. Anal. Math. 19 (1967), 207–215.CrossRefGoogle Scholar
[6]Kotschick, D.. Remarks on geometric structures on compact complex surfaces. Topology 31 (1992), 317–321.CrossRefGoogle Scholar
[7]Raghunathan, M. S.. Discrete subgroups of Lie groups (Springer-Verlag, 1972).CrossRefGoogle Scholar
[8]Wall, C. T. C.. Geometric structures on compact complex surfaces. Topology 25 (1986), 119–153.CrossRefGoogle Scholar
[9]Wang, S. P.. The dual space of semisimple Lie groups. American J.Math. 91 (1969), 921–937.CrossRefGoogle Scholar
[10]Winkelnkemper, H. E.. Un teorema sobre variedades de dimensión 4. Acta Mexicana Ci. Tecn. 2 (1968), 88–89.Google Scholar