An extension of Casson's invariant:
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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[1992]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 126 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400882465 |
| DOI: | 10.1515/9781400882465 |
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| 245 | 1 | 0 | |a An extension of Casson's invariant |c Kevin Walker |
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| 490 | 1 | |a Annals of Mathematics Studies |v number 126 | |
| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) | ||
| 520 | |a 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. | ||
| 546 | |a In English | ||
| 650 | 4 | |a Invariants | |
| 650 | 4 | |a Three-manifolds (Topology) | |
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Datensatz im Suchindex
| _version_ | 1804176498584715264 |
|---|---|
| any_adam_object | |
| author | Walker, Kevin |
| author_facet | Walker, Kevin |
| author_role | aut |
| author_sort | Walker, Kevin |
| author_variant | k w kw |
| building | Verbundindex |
| bvnumber | BV043712506 |
| classification_rvk | SI 830 SK 320 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (ZDB-23-DGG)9781400882465 (OCoLC)1165545309 (DE-599)BVBBV043712506 |
| dewey-full | 514/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.3 |
| dewey-search | 514/.3 |
| dewey-sort | 3514 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400882465 |
| format | Electronic eBook |
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| id | DE-604.BV043712506 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:08Z |
| institution | BVB |
| isbn | 9781400882465 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029124734 |
| oclc_num | 1165545309 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | 1 online resource |
| psigel | ZDB-23-DGG ZDB-23-PST |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Walker, Kevin aut An extension of Casson's invariant Kevin Walker Princeton, NJ Princeton University Press [1992] © 1992 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 126 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) 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. In English Invariants Three-manifolds (Topology) Invariantentheorie (DE-588)4162209-1 gnd rswk-swf Verallgemeinerung (DE-588)4316262-9 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Casson-Invariante (DE-588)4314105-5 gnd rswk-swf Invariante (DE-588)4128781-2 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Invariante (DE-588)4128781-2 s 1\p DE-604 Casson-Invariante (DE-588)4314105-5 s Verallgemeinerung (DE-588)4316262-9 s 2\p DE-604 Invariantentheorie (DE-588)4162209-1 s 3\p DE-604 Erscheint auch als Druck-Ausgabe 0-691-08766-0 Annals of Mathematics Studies number 126 (DE-604)BV040389493 126 https://doi.org/10.1515/9781400882465?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Walker, Kevin An extension of Casson's invariant Annals of Mathematics Studies Invariants Three-manifolds (Topology) Invariantentheorie (DE-588)4162209-1 gnd Verallgemeinerung (DE-588)4316262-9 gnd Dimension 3 (DE-588)4321722-9 gnd Casson-Invariante (DE-588)4314105-5 gnd Invariante (DE-588)4128781-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4162209-1 (DE-588)4316262-9 (DE-588)4321722-9 (DE-588)4314105-5 (DE-588)4128781-2 (DE-588)4037379-4 |
| title | An extension of Casson's invariant |
| title_auth | An extension of Casson's invariant |
| title_exact_search | An extension of Casson's invariant |
| title_full | An extension of Casson's invariant Kevin Walker |
| title_fullStr | An extension of Casson's invariant Kevin Walker |
| title_full_unstemmed | An extension of Casson's invariant Kevin Walker |
| title_short | An extension of Casson's invariant |
| title_sort | an extension of casson s invariant |
| topic | Invariants Three-manifolds (Topology) Invariantentheorie (DE-588)4162209-1 gnd Verallgemeinerung (DE-588)4316262-9 gnd Dimension 3 (DE-588)4321722-9 gnd Casson-Invariante (DE-588)4314105-5 gnd Invariante (DE-588)4128781-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | Invariants Three-manifolds (Topology) Invariantentheorie Verallgemeinerung Dimension 3 Casson-Invariante Invariante Mannigfaltigkeit |
| url | https://doi.org/10.1515/9781400882465?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT walkerkevin anextensionofcassonsinvariant |