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Journal of Topology Advance Access originally published online on November 27, 2008
Journal of Topology 2008 1(4):857-878; doi:10.1112/jtopol/jtn026
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© 2008 London Mathematical Society

Elliptic surfaces without 1-handles

Kouichi Yasui

Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan kyasui@cr.math.sci.osaka-u.ac.jp


  Abstract

Harer-Kas-Kirby conjectured that every handle decomposition of the elliptic surface E(1)2,3 requires both 1- and 3-handles. We prove that the elliptic surface E(n)p,q has a handle decomposition without 1-handles for n ≥ 1 and (p, q) = (2, 3), (2, 5), (3, 4), (4, 5).

Received March 16, 2008.

2000 Mathematics Subject Classification 57R55 (primary), 57R65, 57N13 (secondary)

The author was partially supported by JSPS Research Fellowships for Young Scientists.


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