The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds
We establish a connection between the Alexander polynomial of a knot and its twisted and $L^2$-versions with the triangulations that appear in 3-dimensional hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier matrices of ordered ideal triangulations and use them to provide formul...
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| creator | Garoufalidis, Stavros Yoon, Seokbeom |
| description | We establish a connection between the Alexander polynomial of a knot and its
twisted and $L^2$-versions with the triangulations that appear in 3-dimensional
hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier
matrices of ordered ideal triangulations and use them to provide formulas for
the Alexander polynomial and its variants, the twisted Alexander polynomial and
the $L^2$-Alexander torsion. |
| doi_str_mv | 10.48550/arxiv.2401.01536 |
| format | Article |
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twisted and $L^2$-versions with the triangulations that appear in 3-dimensional
hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier
matrices of ordered ideal triangulations and use them to provide formulas for
the Alexander polynomial and its variants, the twisted Alexander polynomial and
the $L^2$-Alexander torsion.</description><identifier>DOI: 10.48550/arxiv.2401.01536</identifier><language>eng</language><subject>Mathematics - Geometric Topology ; Physics - High Energy Physics - Theory</subject><creationdate>2024-01</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2401.01536$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2401.01536$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Garoufalidis, Stavros</creatorcontrib><creatorcontrib>Yoon, Seokbeom</creatorcontrib><title>The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds</title><description>We establish a connection between the Alexander polynomial of a knot and its
twisted and $L^2$-versions with the triangulations that appear in 3-dimensional
hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier
matrices of ordered ideal triangulations and use them to provide formulas for
the Alexander polynomial and its variants, the twisted Alexander polynomial and
the $L^2$-Alexander torsion.</description><subject>Mathematics - Geometric Topology</subject><subject>Physics - High Energy Physics - Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzz1PwzAUhWEvDKjwA5jw0AEGp3b8lY5VxZcUiSUz0U3uNVhykioJ0Px7oHQ603ukh7EbJTNTWCs3MB7jV5YbqTKprHaXrKw-iN_N33GaCTfr8i1f34tdoiP0SCM_DGnphy5C4kPgEQlSWvg8RujfPxP8NlyLDvoYhoTTFbsIkCa6Pu-KVY8P1f5ZlK9PL_tdKcB5J3xjEeU2RzRASI1qlfUeHHhHyhkI2vgCHfmgm6ClV1hog2Gr2tYbNI1esdv_2xOnPoyxg3Gp_1j1iaV_AGu0R_M</recordid><startdate>20240102</startdate><enddate>20240102</enddate><creator>Garoufalidis, Stavros</creator><creator>Yoon, Seokbeom</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240102</creationdate><title>The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds</title><author>Garoufalidis, Stavros ; Yoon, Seokbeom</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-7b5dd092dd4aedeb1c1577a6a76e164af3478d6e7f3bf3071d834df91cc74d4b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Geometric Topology</topic><topic>Physics - High Energy Physics - Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Garoufalidis, Stavros</creatorcontrib><creatorcontrib>Yoon, Seokbeom</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Garoufalidis, Stavros</au><au>Yoon, Seokbeom</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds</atitle><date>2024-01-02</date><risdate>2024</risdate><abstract>We establish a connection between the Alexander polynomial of a knot and its
twisted and $L^2$-versions with the triangulations that appear in 3-dimensional
hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier
matrices of ordered ideal triangulations and use them to provide formulas for
the Alexander polynomial and its variants, the twisted Alexander polynomial and
the $L^2$-Alexander torsion.</abstract><doi>10.48550/arxiv.2401.01536</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Geometric Topology Physics - High Energy Physics - Theory |
| title | The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds |
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