High-dimensional knot theory : algebraic surgery in codimension 2 / Andrew Ranicki ; with an appendix by Elmar Winkelnkemper.

Format:

Book

Author/Creator:

Ranicki, Andrew, 1948-

Contributor:

Winkelnkemper, Elmar.

Harry E. Humphreys Book Fund.

Series:

Springer monographs in mathematics

Language:

English

Subjects (All):

Knot theory.

Surgery (Topology).

Embeddings (Mathematics).

Physical Description:

xxxvi, 646 pages : illustrations ; 25 cm.

Other Title:

Algebraic surgery in codimension 2

Place of Publication:

Berlin ; New York : Springer, [1998]

Summary:

High-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+2)-dimensional manifolds, generalizing the traditional study of knots in the case n=1. The main theme is the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory. Many results in the research literature are thus brought into a single framework, and new results are obtained. The treatment is particularly effective in dealing with open books, which are manifolds with codimension 2 submanifolds such that the complement fibres over a circle. The book concludes with an appendix by E. Winkelnkemper on the history of open books.

Notes:

Includes bibliographical references (pages [627]-638) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Harry E. Humphreys Book Fund.

ISBN:

3540633898

OCLC:

39189934