A01=Kevin Walker
Absolute value
Andrew Casson
Author_Kevin Walker
Basis (linear algebra)
Category=PBF
Category=PBW
Cohomology
Dan Freed
Dehn surgery
Dehn twist
Determinant
Diagram (category theory)
Disk (mathematics)
Elementary proof
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
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
Product details
- ISBN 9780691025322
- Weight: 198g
- Dimensions: 152 x 235mm
- Publication Date: 23 Mar 1992
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
