@inbook{02309767e4454f41954c3fb7ab36c11d,

title = "Elliptic Three-Manifolds Containing One-Sided Klein Bottles",

abstract = "Extending work of N. Ivanov, the Smale Conjecture is proven for all elliptic three-manifolds containing one-sided Klein bottles, other than the lens space L(4, 1). The technique takes a parameterized family of diffeomorphisms and uses its restriction to embeddings of the Klein bottles to deform the diffeomorphisms to preserve a Seifert fibration of the manifolds. The Conjecture is deduced from this. Another key element of the proof is a collection of techniques for working with parameterized families developed by A. Hatcher.In this chapter, we will prove Theorem 1.3. Section 4.1 gives a construction of the elliptic three-manifolds that contain a one-sided geometrically incompressible Klein bottle; they are described as a family of manifolds M(m, n) that depend on two integer parameters. Section 4.2 is a section-by-section outline of the entire proof, which constitutes the remaining sections of the chapter.",

keywords = "Cone Point, Free Abelian Group, Inverse Image, Isometry Group, Parameterized Family",

author = "Sungbok Hong and John Kalliongis and Darryl McCullough and Rubinstein, {J. Hyam}",

year = "2012",

month = jan,

day = "1",

doi = "10.1007/978-3-642-31564-0_4",

language = "English",

isbn = "9783642315633",

series = "Lecture Notes in Mathematics",

publisher = "Springer Verlag",

pages = "53--83",

booktitle = "Diffeomorphisms of Elliptic 3-Manifolds",

}