Journal of Mathematical Sciences

, Volume 81, Issue 2, pp 2524–2534 | Cite as

Cobordisms of finite quadratic forms and gluing oriented manifolds

  • O. A. Ivanov
  • N. Yu. Netsvetaev
Article
  • 28 Downloads

Abstract

We develop certain discriminant form techniques allowing one to “glue” two integral lattices into a new lattice. In particular, we introduce the notion of fusion of finite forms, which is closely connected with the more familiar notion of cobordism of such forms. We also consider the category of finite forms and their cobordisms. These techniques are used for describing the intersection form of a compact oriented 4k-manifold M obtained by gluing together two manifolds M1 and M2 along one or several boundary components (the intersection forms of M1 and M2 are assumed to be nondegenerate). Bibliography: 12 titles.

Keywords

Manifold Quadratic Form Intersection Form Boundary Component Form Technique 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    O. A. Ivanov, “A construction for integral symmetric bilinear forms,”Zap. Nauchn. Semin. LOMI,83, 63–66 (1979).MATHGoogle Scholar
  2. 2.
    O. A. Ivanov and N. Yu. Netsvetaev, “On the behavior of the intersection form when gluing manifolds along a boundary,” Math. readings in Memory of M.Ya.Suslin, Saratov (1989).Google Scholar
  3. 3.
    O. A. Ivanov and N. Yu. Netsvetaev, “Gluing quadratic forms via gluing oriented manifolds,” Int. conf. on algebra in mem. Shirshov, Novosibirsk (1991), p. 14.Google Scholar
  4. 4.
    V. V. Nikulin, “Integral symmetric bilinear forms and some of their geometric applications,”Izv. Akad. Nauk SSSR, Ser. Math.,43, 111–177 (1979).MATHMathSciNetGoogle Scholar
  5. 5.
    G. M. Brumfiel and J. M. Morgan, “Quadratic functions, the index modulo 8 and a ℤ/4-Hirzebruch formula,”Topology,12, 105–122 (1973).CrossRefMathSciNetGoogle Scholar
  6. 6.
    J. Barge, J. Lannes, F. Latour, and P. Vogel, “Λ-spheres,”Ann. Scient. Ec. Norm. Sup., (4e serie), 4, 463–506 (1974).MathSciNetGoogle Scholar
  7. 7.
    J. Lannes, “Forms quandratiques d'enlacement sur l'anneau des entiers d'une corps de nombres,”Ann. Scient. Ec. Norm. Sup., (4e serie),8, 535–579 (1975).MATHMathSciNetGoogle Scholar
  8. 8.
    W. Scharlau,Quadratic and Hermitian Forms, Springer-Verlag, Berlin-New York (1985).Google Scholar
  9. 9.
    A. Dimca, “On the homology and cohomology of complete intersections with isolated singularities,”Compositio Math.,58, 321–339 (1986).MATHMathSciNetGoogle Scholar
  10. 10.
    J. H. Conway and N. J. A. Sloane,Sphere packings, Lattices and Groups, Springer-Verlag, Berlin-New York (1988).Google Scholar
  11. 11.
    O. Ya. Viro,Branched coverings of manifolds with boundary, Ph. D. Thesis, Leningrad (1974).Google Scholar
  12. 12.
    J. Levine, “Knot cobordism groups in codimension two,”Com. Math. Helv.,44, 229–244 (1969).MATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • O. A. Ivanov
  • N. Yu. Netsvetaev

There are no affiliations available

Personalised recommendations