
An Extension of Casson's Invariant
An Extension of Casson's Invariant. (AM-126)
Kevin Walker(Author)
Princeton University Press
Published on 23. March 1992
Book
Paperback/Softback
150 pages
978-0-691-02532-2 (ISBN)
Description
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.
Reviews / Votes
"[This is] a monograph describing Walker's extension of Casson's invariant to Q HS ... This is a fascinating subject and Walker's book is informative and well written ... it makes a rather pleasant introduction to a very active area in geometric topology."--Bulletin of the American Mathematical SocietyMore details
Series
Language
English
Place of publication
New Jersey
United States
Target group
Professional and scholarly
College/higher education
Product notice
Paperback (trade)
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 8 mm
Weight
225 gr
ISBN-13
978-0-691-02532-2 (9780691025322)
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Schweitzer Classification
Other editions
Additional editions

Kevin Walker
An Extension of Casson's Invariant
Extension of Casson's Invariant. (AM-126), Volume 126
E-Book
06/2016
1st Edition
Princeton University Press
€79.49
Available for download
Person
Kevin Walker
Content
*Frontmatter, pg. i*Contents, pg. v*0. Introduction, pg. 1*1. Topology of Representation Spaces, pg. 6*2. Definition of lambda, pg. 27*3. Various Properties of lambda, pg. 41*4. The Dehn Surgery Formula, pg. 81*5. Combinatorial Definition of lambda, pg. 95*6. Consequences of the Dehn Surgery Formula, pg. 108*A. Dedekind Sums, pg. 113*B. Alexander Polynomials, pg. 122*Bibliography, pg. 129