By Symposium in Pure Mathematics Stanford University 1976, Visit Amazon's R. James Milgram Page, search results, Learn about Author Central, R. James Milgram, , American Mathematical Society

ISBN-10: 082181432X

ISBN-13: 9780821814321

ISBN-10: 0821814737

ISBN-13: 9780821814734

Includes sections on Algebraic $K$- and $L$-theory, surgical procedure and its purposes, team activities

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Surgering the torus S ∪ A via D yields a sphere, which bounds a ball in M since M is irreducible. Hence S ∪ A bounds a solid torus and S is ∂ -parallel, being isotopic to A (rel ∂S ). 5. , transverse to all fibers. Proof: Let C1 , · · · , Cn (n ≥ 1) be fibers of the Seifert fibering which include all the multiple fibers, and let M0 be M with small fibered open tubular neighborhoods of all the Ci ’s deleted. M0 is then a circle bundle π : M0 → B0 over a compact surface B0 with ∂B0 = ∅ . Choose disjoint arcs in B0 whose union splits B0 into a disk (we may assume 32 Torus Decomposition Ch.

2) Eliminate arcs of S ∩ σ 2 with both endpoints on the same edge of σ 2 , by isotopy of S. After these simplifications, components of M || S meeting 2-simplices only in rectangles are I -bundles (disjoint from ∂M ), as before. Trivial I -bundles are ruled out by hypothesis (assuming n ≥ 2 , so that M is not a fiber bundle with fiber S = S1 ), while nontrivial I bundles are tubular neighborhoods of 1-sided (hence nonseparating) surfaces T1 , · · · , Tm , say. We may assume M is connected, and then reorder the components Si of S so that M | (S1 ∪ · · · ∪ Sk ) is connected and each of Sk+1 , · · · , Sn separates M | (S1 ∪ · · · ∪ Sk ) .

40 Seifert Manifolds Ch. 4 Chapter 4. Seifert Manifolds Seifert manifolds, introduced in the last chapter where they play a special role in the torus decomposition, are among the best-understood 3-manifolds. In this chapter our goal is the classification of orientable Seifert manifolds up to diffeomorphism. We begin with the classification up to fiber-preserving diffeomorphism, which is fairly straightforward. Then we show that in most cases the Seifert fibering is unique, so in these cases the diffeomorphism and fiber-preserving diffeomorphism classifications coincide.

### Algebraic and geometric topology by Symposium in Pure Mathematics Stanford University 1976, Visit Amazon's R. James Milgram Page, search results, Learn about Author Central, R. James Milgram, , American Mathematical Society

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