Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-25T17:24:15.861Z Has data issue: false hasContentIssue false
  • English
  • Français

On bilinear forms represented by trees

Published online by Cambridge University Press:  17 April 2009

Walter D. Neumann
Walter D. Neumann
Affiliation:
Department of Mathematics, Ohio State University, Columbus, OH 43210, United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The adjacency matrix of a weighted graph determines an integral bilinear form. The trees with unimodular adjacency matrices are described with special emphasis on the definite and semidefinite cases, since they arise as configuration graphs of good divisors in compact complex surfaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 2 , October 1989 , pp. 303 - 321
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Conway, J.H.C. and Sloane, N.J.A., ‘On the enumeration of lattices of determinant 1’, J. Number Theory 15 (1982), 83–94.Google Scholar
[2]Conway, J.H.C. and Sloane, N.J.A., ‘The unimodular lattices of dimension up to 23 and the Minkowski-Siegel mass constants’, European J. Combin. 3 (1982), 219–231.Google Scholar
[3]Eisenbud, D. and Neumann, W.D., Three-Dimensional Link Theory and Invariants of Plane Curve Singularities, Annals of Math. Studies 110 (Princeton Univ. Press, 1985).Google Scholar
[4]Kneser, M., ‘Klassenzahlen definiter quadratischer Formen’, Arch. Math. 8 (1957), 241–250.Google Scholar
[5]Neumann, W.D., ‘A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves’, Trans. Amer. Math. Soc. 268 (1981), 299–343.CrossRefGoogle Scholar
[6]Neumann, W.D., ‘On the topology of curves in complex surfaces’: Proceedings of Conference on Topological Methods in Algebraic Transformation Groups. Progress in Math (Birkhäser Verlag). (to appear)Google Scholar
[7]Neumann, W.D., ‘Links of curves in compact complex surfaces’, (in preparation).Google Scholar
[8]Neumann, W.D. and Zagier, D., ‘A note on an invariant of Fintushel and Stern’: Proc. Special Year in Topology Maryland 1983/4. Lecture Notes in Mathematics 1167, pp. 241–244 (Springer-Verlag, Berlin, Heidelberg, New York).Google Scholar
[9]Niemeier, H-V, ‘Definite quadratische Formen der Dimension 24 und Diskriminante 1’, J. Number Theory 5 (1973), 142–178.CrossRefGoogle Scholar
[10]Petrie, T. and Dieck, T. tom, ‘Homology planes and announcement and survey’: Proceedings of Conference on Topological Methods in Algebraic Transformation Groups. Progress in Math (Birkhäser Verlag). (to appear)Google Scholar
[11]Serre, J.P., A Course in Arithmetic, Graduate Texts in Mathematics 7 (Springer-Verlag, Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar
[12]Siebenmann, L., On the vanishing of the Rohlin inveriant and non-finitely amphicheiral homology 3-spheres: Topology Symposium, Siegen 1979, Koschorke, and Neumann, , ed. Lecture Notes in Mathematics 788, p 172–222 (Springer-Verlag, Berlin, Heidelberg, New York).Google Scholar
[13]Waldhausen, F., ‘On irreducible 3-manifolds that are sufficiently large’, Ann. of Math. 87 (1968), 56–88.CrossRefGoogle Scholar
[14]Yamada, Akio and Matsumoto, Yukio, ‘On the resolution diagrams of Brieskorn singularities (2,q, r) of type II’, Canad. J. Math. 35 (1983), 1049–1058.CrossRefGoogle Scholar