One-sided heegaard splittings of 3-manifolds

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. © 1978, University of California, Berkeley. All Rights Reserved.