An Extension of Casson's Invariant (eBook)

Kevin Walker (Autor)

eBook Download: PDF

2016
Princeton University Press (Verlag)
978-1-4008-8246-5 (ISBN)

Infos

This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be an appropriately defined intersection number of R(W) and R(W) inside R(F). The definition of this intersection number is a delicate task, as the spaces involved have singularities. A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: absolute value • Andrew Casson • Basis (linear algebra) • cohomology • Dan Freed • Dehn surgery • Dehn twist • Determinant • Diagram (category theory) • Disk (mathematics) • Elementary proof • fundamental group • General position • Heegaard splitting • homology sphere • Identity matrix • Inner product space • Lie group • Mathematical Sciences • Morris Hirsch • Normal bundle • scientific notation • Sequence • Surjective function • Symplectic Geometry • Theorem • Topology
• ISBN-10: 1-4008-8246-X / 140088246X
• ISBN-13: 978-1-4008-8246-5 / 9781400882465