Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 /

Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 / / Christine Lescop.

This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F con...

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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Lescop, Christine,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2014]
©1996
Year of Publication:2014
Language:English
Series:Annals of Mathematics Studies ; 140
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spelling Lescop, Christine, author. aut http://id.loc.gov/vocabulary/relators/aut
Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 / Christine Lescop.
Princeton, NJ : Princeton University Press, [2014]
©1996
1 online resource (150 p.)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Annals of Mathematics Studies ; 140
Frontmatter -- Table of contents -- Chapter 1. Introduction and statements of the results -- Chapter 2. The Alexander series of a link in a rational homology sphere and some of its properties -- Chapter 3. Invariance of the surgery formula under a twist homeomorphism -- Chapter 4. The formula for surgeries starting from rational homology spheres -- Chapter 5. The invariant A. for 3-manifolds with nonzero rank -- Chapter 6. Applications and variants of the surgery formula -- Appendix. More about the Alexander series -- Bibliography -- Index
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)
MATHEMATICS / Topology. bisacsh
3-manifold.
Addition.
Alexander polynomial.
Ambient isotopy.
Betti number.
Casson invariant.
Change of basis.
Change of variables.
Cobordism.
Coefficient.
Combination.
Combinatorics.
Computation.
Conjugacy class.
Connected component (graph theory).
Connected space.
Connected sum.
Cup product.
Determinant.
Diagram (category theory).
Disk (mathematics).
Empty set.
Exterior (topology).
Fiber bundle.
Fibration.
Function (mathematics).
Fundamental group.
Homeomorphism.
Homology (mathematics).
Homology sphere.
Homotopy sphere.
Indeterminate (variable).
Integer.
Klein bottle.
Knot theory.
Manifold.
Morphism.
Notation.
Orientability.
Permutation.
Polynomial.
Prime number.
Projective plane.
Scientific notation.
Seifert surface.
Sequence.
Summation.
Symmetrization.
Taylor series.
Theorem.
Topology.
Tubular neighborhood.
Unlink.
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496
print 9780691021324
https://doi.org/10.1515/9781400865154
https://www.degruyter.com/isbn/9781400865154
Cover https://www.degruyter.com/document/cover/isbn/9781400865154/original
language English
format eBook
author Lescop, Christine,
Lescop, Christine,
spellingShingle Lescop, Christine,
Lescop, Christine,
Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 /
Annals of Mathematics Studies ;
Frontmatter --
Table of contents --
Chapter 1. Introduction and statements of the results --
Chapter 2. The Alexander series of a link in a rational homology sphere and some of its properties --
Chapter 3. Invariance of the surgery formula under a twist homeomorphism --
Chapter 4. The formula for surgeries starting from rational homology spheres --
Chapter 5. The invariant A. for 3-manifolds with nonzero rank --
Chapter 6. Applications and variants of the surgery formula --
Appendix. More about the Alexander series --
Bibliography --
Index
author_facet Lescop, Christine,
Lescop, Christine,
author_variant c l cl
c l cl
author_role VerfasserIn
VerfasserIn
author_sort Lescop, Christine,
title Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 /
title_full Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 / Christine Lescop.
title_fullStr Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 / Christine Lescop.
title_full_unstemmed Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 / Christine Lescop.
title_auth Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 /
title_alt Frontmatter --
Table of contents --
Chapter 1. Introduction and statements of the results --
Chapter 2. The Alexander series of a link in a rational homology sphere and some of its properties --
Chapter 3. Invariance of the surgery formula under a twist homeomorphism --
Chapter 4. The formula for surgeries starting from rational homology spheres --
Chapter 5. The invariant A. for 3-manifolds with nonzero rank --
Chapter 6. Applications and variants of the surgery formula --
Appendix. More about the Alexander series --
Bibliography --
Index
title_new Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 /
title_sort global surgery formula for the casson-walker invariant. (am-140), volume 140 /
series Annals of Mathematics Studies ;
series2 Annals of Mathematics Studies ;
publisher Princeton University Press,
publishDate 2014
physical 1 online resource (150 p.)
Issued also in print.
contents Frontmatter --
Table of contents --
Chapter 1. Introduction and statements of the results --
Chapter 2. The Alexander series of a link in a rational homology sphere and some of its properties --
Chapter 3. Invariance of the surgery formula under a twist homeomorphism --
Chapter 4. The formula for surgeries starting from rational homology spheres --
Chapter 5. The invariant A. for 3-manifolds with nonzero rank --
Chapter 6. Applications and variants of the surgery formula --
Appendix. More about the Alexander series --
Bibliography --
Index
isbn 9781400865154
9783110494914
9783110442496
9780691021324
url https://doi.org/10.1515/9781400865154
https://www.degruyter.com/isbn/9781400865154
https://www.degruyter.com/document/cover/isbn/9781400865154/original
illustrated Not Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 514 - Topology
dewey-full 514
dewey-sort 3514
dewey-raw 514
dewey-search 514
doi_str_mv 10.1515/9781400865154
oclc_num 887802708
work_keys_str_mv AT lescopchristine globalsurgeryformulaforthecassonwalkerinvariantam140volume140
status_str n
ids_txt_mv (DE-B1597)447742
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carrierType_str_mv cr
hierarchy_parent_title Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
is_hierarchy_title Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 /
container_title Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
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