Character varieties of higher dimensional representations and splittings of 3-manifolds
In 1983 Culler and Shalen established a way to construct essential surfaces in a 3-manifold from ideal points of the SL 2 -character variety associated to the 3-manifold group. We present in this article an analogous construction of certain kinds of branched surfaces (which we call essential tribran...
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| Veröffentlicht in: | Geometriae dedicata 2021, Vol.213 (1), p.433-466 |
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| container_title | Geometriae dedicata |
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| creator | Hara, Takashi Kitayama, Takahiro |
| description | In 1983 Culler and Shalen established a way to construct essential surfaces in a 3-manifold from ideal points of the
SL
2
-character variety associated to the 3-manifold group. We present in this article an analogous construction of certain kinds of branched surfaces (which we call
essential tribranched surfaces
) from ideal points of the
SL
n
-character variety for a natural number
n
greater than or equal to 3. Further we verify that such a branched surface induces a nontrivial presentation of the 3-manifold group in terms of the fundamental group of a certain 2-dimensional complex of groups. |
| doi_str_mv | 10.1007/s10711-020-00590-y |
| format | Article |
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SL
2
-character variety associated to the 3-manifold group. We present in this article an analogous construction of certain kinds of branched surfaces (which we call
essential tribranched surfaces
) from ideal points of the
SL
n
-character variety for a natural number
n
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SL
2
-character variety associated to the 3-manifold group. We present in this article an analogous construction of certain kinds of branched surfaces (which we call
essential tribranched surfaces
) from ideal points of the
SL
n
-character variety for a natural number
n
greater than or equal to 3. Further we verify that such a branched surface induces a nontrivial presentation of the 3-manifold group in terms of the fundamental group of a certain 2-dimensional complex of groups.</description><subject>Algebraic Geometry</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Hyperbolic Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Projective Geometry</subject><subject>Topology</subject><issn>0046-5755</issn><issn>1572-9168</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEUxIMoWKtfwNOC5-hL0mx2j1L8BwUviseQTd62KdvdNUmFfntjV_DmuzwYZobhR8g1g1sGoO4iA8UYBQ4UQNZADydkxqTitGZldUpmAIuSSiXlObmIcQsAtVJ8Rj6WGxOMTRiKLxM8Jo-xGNpi49ebrDm_wz76oTddEXAMGLFPJmUhFqZ3RRw7n5Lv18eQoDvT-3boXLwkZ63pIl79_jl5f3x4Wz7T1evTy_J-Ra0QZaIqr3OIToFwVeMUc6WqmrLkYJRCrsA4wbjl2JqKKyPsov2RrG0ayWpuxJzcTL1jGD73GJPeDvuQ50bN5UKKMh9kF59cNgwxBmz1GPzOhINmoH8A6gmgzgD1EaA-5JCYQjGb-zWGv-p_Ut9HEXVZ</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Hara, Takashi</creator><creator>Kitayama, Takahiro</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-2588-3455</orcidid></search><sort><creationdate>2021</creationdate><title>Character varieties of higher dimensional representations and splittings of 3-manifolds</title><author>Hara, Takashi ; Kitayama, Takahiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c336t-7168deed703d8bd71d678b6620a77e270ad312c2efa827a3c4f0ad3ccbb5192a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algebraic Geometry</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Hyperbolic Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Projective Geometry</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hara, Takashi</creatorcontrib><creatorcontrib>Kitayama, Takahiro</creatorcontrib><collection>CrossRef</collection><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hara, Takashi</au><au>Kitayama, Takahiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Character varieties of higher dimensional representations and splittings of 3-manifolds</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2021</date><risdate>2021</risdate><volume>213</volume><issue>1</issue><spage>433</spage><epage>466</epage><pages>433-466</pages><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>In 1983 Culler and Shalen established a way to construct essential surfaces in a 3-manifold from ideal points of the
SL
2
-character variety associated to the 3-manifold group. We present in this article an analogous construction of certain kinds of branched surfaces (which we call
essential tribranched surfaces
) from ideal points of the
SL
n
-character variety for a natural number
n
greater than or equal to 3. Further we verify that such a branched surface induces a nontrivial presentation of the 3-manifold group in terms of the fundamental group of a certain 2-dimensional complex of groups.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-020-00590-y</doi><tpages>34</tpages><orcidid>https://orcid.org/0000-0003-2588-3455</orcidid></addata></record> |
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| source | SpringerNature Complete Journals |
| subjects | Algebraic Geometry Convex and Discrete Geometry Differential Geometry Hyperbolic Geometry Mathematics Mathematics and Statistics Original Paper Projective Geometry Topology |
| title | Character varieties of higher dimensional representations and splittings of 3-manifolds |
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