An Extension of Casson's Invariant. (AM-126), Volume 126 / / Kevin Walker.
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...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1992 |
Year of Publication: | 2016 |
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Walker, Kevin, author. aut http://id.loc.gov/vocabulary/relators/aut An Extension of Casson's Invariant. (AM-126), Volume 126 / Kevin Walker. Princeton, NJ : Princeton University Press, [2016] ©1992 1 online resource (150 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 126 Frontmatter -- Contents -- 0. Introduction -- 1. Topology of Representation Spaces -- 2. Definition of λ -- 3. Various Properties of λ -- 4. The Dehn Surgery Formula -- 5. Combinatorial Definition of λ -- 6. Consequences of the Dehn Surgery Formula -- A. Dedekind Sums -- B. Alexander Polynomials -- Bibliography restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. 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) Invariants. Three-manifolds (Topology). MATHEMATICS / Topology. bisacsh Absolute value. Andrew Casson. Basis (linear algebra). Cohomology. Dan Freed. Dehn surgery. Dehn twist. Determinant. Diagram (category theory). Disk (mathematics). Elementary proof. 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. 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 9780691025322 https://doi.org/10.1515/9781400882465 https://www.degruyter.com/isbn/9781400882465 Cover https://www.degruyter.com/document/cover/isbn/9781400882465/original |
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English |
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Walker, Kevin, Walker, Kevin, |
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Walker, Kevin, Walker, Kevin, An Extension of Casson's Invariant. (AM-126), Volume 126 / Annals of Mathematics Studies ; Frontmatter -- Contents -- 0. Introduction -- 1. Topology of Representation Spaces -- 2. Definition of λ -- 3. Various Properties of λ -- 4. The Dehn Surgery Formula -- 5. Combinatorial Definition of λ -- 6. Consequences of the Dehn Surgery Formula -- A. Dedekind Sums -- B. Alexander Polynomials -- Bibliography |
author_facet |
Walker, Kevin, Walker, Kevin, |
author_variant |
k w kw k w kw |
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VerfasserIn VerfasserIn |
author_sort |
Walker, Kevin, |
title |
An Extension of Casson's Invariant. (AM-126), Volume 126 / |
title_full |
An Extension of Casson's Invariant. (AM-126), Volume 126 / Kevin Walker. |
title_fullStr |
An Extension of Casson's Invariant. (AM-126), Volume 126 / Kevin Walker. |
title_full_unstemmed |
An Extension of Casson's Invariant. (AM-126), Volume 126 / Kevin Walker. |
title_auth |
An Extension of Casson's Invariant. (AM-126), Volume 126 / |
title_alt |
Frontmatter -- Contents -- 0. Introduction -- 1. Topology of Representation Spaces -- 2. Definition of λ -- 3. Various Properties of λ -- 4. The Dehn Surgery Formula -- 5. Combinatorial Definition of λ -- 6. Consequences of the Dehn Surgery Formula -- A. Dedekind Sums -- B. Alexander Polynomials -- Bibliography |
title_new |
An Extension of Casson's Invariant. (AM-126), Volume 126 / |
title_sort |
an extension of casson's invariant. (am-126), volume 126 / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (150 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- 0. Introduction -- 1. Topology of Representation Spaces -- 2. Definition of λ -- 3. Various Properties of λ -- 4. The Dehn Surgery Formula -- 5. Combinatorial Definition of λ -- 6. Consequences of the Dehn Surgery Formula -- A. Dedekind Sums -- B. Alexander Polynomials -- Bibliography |
isbn |
9781400882465 9783110494914 9783110442496 9780691025322 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA613 |
callnumber-sort |
QA 3613 |
url |
https://doi.org/10.1515/9781400882465 https://www.degruyter.com/isbn/9781400882465 https://www.degruyter.com/document/cover/isbn/9781400882465/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514/.3 |
dewey-sort |
3514 13 |
dewey-raw |
514/.3 |
dewey-search |
514/.3 |
doi_str_mv |
10.1515/9781400882465 |
oclc_num |
979743249 |
work_keys_str_mv |
AT walkerkevin anextensionofcassonsinvariantam126volume126 AT walkerkevin extensionofcassonsinvariantam126volume126 |
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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 |
An Extension of Casson's Invariant. (AM-126), Volume 126 / |
container_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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