Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$

Abstract


 The present paper investigates Heegaard diagrams of non-orientable closed $3$-manifolds, i.e. a non-orienable closed surface together with two sets of meridian disks of both handlebodies.
 It is found all possible non-orientable genus $2$ Heegaard diagrams of complexity less than $6$.
 Topological properties of Morse flows on closed smooth non-orientable $3$-manifolds are described.
 Normalized Heegaard diagrams are furhter used for classification Morse flows with a minimal number of singular points and singular trajectories