Wolfgang Heil
PhD, Rice University (Houston,Tx), 1970

Topology of 3-manifolds

(1) Construction of 3-manifolds: Starting with well-known pieces (e.g. balls, handlebodies of genus 1, Seifert fiber spaces) which manifolds are obtained from these by cutting and pasting (e.g. by Dehn surgery or by gluing the pieces along surfaces in their boundaries)? In particular, which non-orientable manifolds are obtained as a union of two or three orientable pieces? (2) Fundamental groups of 3-manifolds: Which groups are fundamental groups of 3-manifolds? (3) A-category of manifolds. For a given CW-complex A, which manifolds are of A-category 2 or 3? We have solved the case for A-category 2 when A is a 1-sphere, a 2-sphere or projective plane.