These are notes for a lecture series given at the University
of Oslo in 1971 - 1972. Although the manifolds of the title ?;ere
constructed by Seifert [1] in 1933, considerable interest has
been devoted to them recently. The principal aim here is to
survey the new results and to emphasize the variety of areas and
techniques involved.
The equivariant theory comprising the first four chapters
was initiated by Raymond [1], who discovered that two classes of
Seifert manifolds coincide with certain fixed point free 3-dimen-
sional S -manifolds. Chapter 1 contains Raymond's
classification of S -actions on 3-nianifolds. Chapter 2 describes equivar-
2
iant plumbing of D -bundles over 2-manifolds and identifies the
boundary 3-manifolds, This is used in chapter 3 to resolve
singularities of complex algebraic surfaces with C*-action. The
technique is to compute the Seifert invariants of a suitable
neighborhood boundary of the singular point and use these to
construct an equivariant resolution following Orlik-Wagreich [1,2],
The equivariant fixed point free cobordism classification of
Seifert manifolds due to Ossa [1] is given in chapter 4.