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" 3manifolds (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. 0* Introduction* In [7] an example is given showing that the loop theorem is not valid for one-sided surfaces in 3-manifolds. For this reason, such surfaces are difficult to handle and have not been the object of much work. We would like to present a new approach based on the following: