Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-06-09T04:50:57.083Z Has data issue: false hasContentIssue false
  • English
  • Français

Homotopy Self-Equivalences of 4-manifolds with Free Fundamental Group

Published online by Cambridge University Press:  20 November 2018

Mehmetcik Pamuk
Mehmetcik Pamuk*
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, ON
*
mpamuk@metu.edu.tr
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 calculate the group of homotopy classes of homotopy self-equivalences of 4-manifolds with free fundamental group and obtain a classification of such 4-manifolds up to s-cobordism.

Keywords

57N1355P1057R80
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 6 , 14 December 2010 , pp. 1387 - 1403
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Brown, K. S., Cohomology of groups. Corrected reprint of the 1982 original, Graduate Texts in Mathematics, 87, Springer-Verlag, New York, 1994.Google Scholar
[2] Cavicchioli, A. and Hegenbarth, F., On 4-manifolds with free fundamental group. Forum Math. 6(1994), no. 4, 415–429. doi:10.1515/form.1994.6.415Google Scholar
[3] Cavicchioli, A., Hegenbarth, F., and Repovs, D., Four-manifolds with surface fundamental groups. Trans. Amer. Math. Soc. 349(1997), no. 10, 4007–4019. doi:10.1090/S0002-9947-97-01751-0Google Scholar
[4] Hambleton, I. and Kreck, M., On the classification of topological 4-manifolds with finite fundamental group. Math. Ann. 280(1988), no. 1, 85–104. doi:10.1007/BF01474183Google Scholar
[5] Hambleton, I. and Kreck, M., Homotopy self-equivalences of 4-manifolds. Math. Z. 248(2004), no. 1, 147–172. doi:10.1007/s00209-004-0657-9Google Scholar
[6] Hatcher, A., Algebraic topology, Cambridge University Press, Cambridge, 2002.Google Scholar
[7] Hillman, J. A., Four-manifolds, geometries and knots. Geometry & Topology Monographs, 5, Geometry & Topology Publications, Coventry, 2002.Google Scholar
[8] Hillman, J. A., PD4-complexes with free fundamental group. Hiroshima Math. J. 34(2004), no. 3, 295–306.Google Scholar
[9] Hillman, J. A., PD4-complexes with strongly minimal models. Topology Appl. 153(2006), no. 14, 2413–2424. doi:10.1016/j.topol.2005.09.002Google Scholar
[10] Kreck, M., Surgery and duality. Ann. of Math. (2) 149(1999), no. 3, 707–754. doi:10.2307/121071Google Scholar
[11] Møller, J. M., Self-homotopy equivalences of group cohomology spaces. J. Pure Appl. Algebra 73(1991), no. 1, 23–37. doi:10.1016/0022-4049(91)90104-AGoogle Scholar
[12] Pamuk, M., Homotopy self-equivalences of 4-manifolds. Ph. D. Thesis, Mc Master University, 2008.Google Scholar
[13] Stallings, J., Whitehead torsion of free products. Ann. of Math. 82(1965), 354–363. doi:10.2307/1970647Google Scholar
[14] Teichner, P., On the signature of four-manifolds with universal covering spin. Math. Ann. 295(1993), no. 4, 745–759. doi:10.1007/BF01444915Google Scholar
[15] Wall, C. T. C., Surgery on compact manifolds. Second ed., Mathematical Surveys and Monographs, 69, American Mathematical Society, Providence, RI, 1999.Google Scholar
[16] Whitehead, J. H. C., A certain exact sequence. Ann. of Math. 52(1950), 51–110. doi:10.2307/1969511Google Scholar