| An Extension of Casson's Invariant. (Am-126), Volume 126 Contributor(s): Walker, Kevin (Author) |
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ISBN: 0691025320 ISBN-13: 9780691025322 Publisher: Princeton University Press OUR PRICE: $70.30 Product Type: Paperback - Other Formats Published: March 1992 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General - Science |
| Dewey: 514.3 |
| LCCN: 91042226 |
| Physical Information: 0.39" H x 6.17" W x 9.25" (0.48 lbs) 150 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |