One-sided Heegaard splittings of 3-manifolds

J. Hyam Rubinstein

Vol. 76 (1978), No. 1, 185–200

DOI: 10.2140/pjm.1978.76.185

Abstract

For a large class of closed orientable 3-manifolds, we define a new decomposition method which uses embedded one-sided surfaces and is analogous to Heegaard splittings. The technique is most useful for studying some “small” 3-manifolds (i.e., which have finite fundamental group or are not sufficiently large). We give several general criteria for existence of these splittings and some results on nonorientable surfaces in lens spaces. Also stable equivalence (as for Heegaard splittings) and a result of Waldhausen’s are shown to carry over to the one-sided case.

Mathematical Subject Classification

Primary: 57A10, 57A10

Milestones

Received: 15 January 1977

Revised: 23 June 1977

Published: 1 May 1978