Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T02:03:34.926Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stable classification of certain 4-manifolds

Published online by Cambridge University Press:  17 April 2009

Alberto Cavicchioli ,
Friedrich Hegenbarth  and
Dušan Repovš
Alberto Cavicchioli
Affiliation:
Dipartimento di MatematicaUniversità di Modena41100 ModenaItaly, e-mail: Dipmat@imoax1.unimo.it
Friedrich Hegenbarth
Affiliation:
Dipartimento di MatematicaUniversità di Milano20133 MilanoItaly, e-mail: Dipmat@imiucca.csi.unimi.it
Dušan Repovš
Affiliation:
Institute of MathematicsPhysics and MechanicsUniversity of LjubljanaLjubljana 61111Slovenia, e-mail: Dusan.Repovs@unilj.si
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.

We study the s-cobordism type of closed orientable (smooth or PL) 4–manifolds with free or surface fundamental groups. We prove stable classification theorems for these classes of manifolds by using surgery theory.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 3 , December 1995 , pp. 385 - 398
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Bauer, S., The Homotopy type of a 4-manifold with finite fundamental group, Lecture Notes in Mathematics 1361 (Springer-Verlag, Berlin, Heidelberg, New York, 1988).Google Scholar
[2]Baues, H.J., Combinatorial homotopy and 4-dimensional complexes (Walter de Gruyter, Berlin, New York, 1991).CrossRefGoogle Scholar
[3]Cappell, S.E. and Shaneson, J.L., ‘On four-dimensional surgery and applications’, Comment. Math. Helv. 46 (1971), 500–528.CrossRefGoogle Scholar
[4]Cappell, S.E., ‘Mayer-Vietoris sequences in Hermitian K-theory’, in Proc. Conf. Battelle Memorial Inst., Seattle, Wash., 1972, (Springer-Verlag, Berlin, Heidelberg, New York, 1973), pp. 478–512.Google Scholar
[5]Cavicchioli, A. and Hegenbarth, F., ‘On the intersection forms of closed 4-manifolds’, Publ. Mat. 36 (1992), 73–83.CrossRefGoogle Scholar
[6]Cavicchioli, A. and Hegenbarth, F., ‘On 4-manifolds with free fundamental group’, Forum Math. 6 (1994), 415–429.CrossRefGoogle Scholar
[7]Cavicchioli, A., Hegenbarth, F. and Repovš, D., ‘Four-manifolds with surface fundamental groups’ (to appear).Google Scholar
[8]Cochran, T.D. and Habegger, N., ‘On the homotopy theory of simply-connected four manifolds’, Topology 29 (1990), 419–440.CrossRefGoogle Scholar
[9]Donaldson, S.K., ‘The orientation of Yang-Mills moduli spaces and 4-manifold topology’, J. Differential Geom. 26 (1987), 397–428.CrossRefGoogle Scholar
[10]Freedman, M.H., ‘The topology of 4-manifolds’, J. Differential Geom. 17 (1982), 357–453.CrossRefGoogle Scholar
[11]Freedman, M.H. and Quinn, F., Topology of 4-manifolds (Princeton Univ. Press, Princeton, New Jersey, 1990).Google Scholar
[12]Hambleton, I. and Kreck, M., ‘On the classification of topological 4-manifolds with finite fundamental group’, Math. Ann. 280 (1988), 85–104.CrossRefGoogle Scholar
[13]Hillman, J.A., ‘On 4-manifolds homotopy equivalent to surface bundles over surfaces’, Topology Appl. 40 (1991), 275–286.CrossRefGoogle Scholar
[14]Hillman, J.A., ‘Free products and 4-dimensional connected sums’ (to appear).Google Scholar
[15]Kirby, R.C. and Siebenmann, L.C., Foundational essays on topological manifolds, smoothings and triangulations, Ann. of Math. Studies 88 (Princeton Univ. Press, Princeton, New Jersey, 1977).CrossRefGoogle Scholar
[16]Mandelbaum, R., ‘Four-dimensional topology: an introduction’, Bull. Amer. Math. Soc. 2 (1980), 1–159.CrossRefGoogle Scholar
[17]Milnor, J., ‘Whitehead torsion’, Bull. Amer. Math. Soc. 72 (1966), 358–426.CrossRefGoogle Scholar
[18]Shaneson, J.L., ‘Non-simply connected surgery and some results in low dimension topology’, Comment. Math. Helv. 45 (1970), 333–352.CrossRefGoogle Scholar
[19]Shaneson, J.L., ‘On non-simply connected manifolds’, in Proc. Sympos. Pure Math. 22 (Amer. Math. Soc, Providence, R.I., 1970), pp. 221–229.Google Scholar
[20]Sullivan, D., ‘Triangulating and smoothing homotopy equivalences and homeomorphisms’, in Geometric Topology Sem. Notes (Princeton Univ. Press, Princeton, New Jersey, 1967).Google Scholar
[21]Thorn, R., ‘Quelques propriétés globales des variétés’, Comment. Math. Helv. 28 (1954), 17–86.Google Scholar
[22]Wall, C.T.C., ‘On simply connected 4-manifolds’, J. London Math. Soc. 39 (1964), 141–149.CrossRefGoogle Scholar
[23]Wall, C.T.C., Surgery on Compact Manifolds (Academic Press, London, New York, 1970).Google Scholar