A new proof of the growth rate of the solvable Baumslag–Solitar groups
We exhibit a regular language of geodesics for a large set of elements of BS (1, n ) and show that the growth rate of this language is the growth rate of the group. This provides a straightforward calculation of the growth rate of BS (1, n ), which was initially computed by Collins et al. (AM (Bas...
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| Veröffentlicht in: | Geometriae dedicata 2022-04, Vol.216 (2), Article 22 |
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| creator | Taback, Jennifer Walker, Alden |
| description | We exhibit a regular language of geodesics for a large set of elements of
BS
(1,
n
) and show that the growth rate of this language is the growth rate of the group. This provides a straightforward calculation of the growth rate of
BS
(1,
n
), which was initially computed by Collins et al. (AM (Basel) 62:1-11, 1994). Our methods are based on those we develop in Taback and Walker (JTA, to appear) to show that
BS
(1,
n
) has a positive density of elements of positive, negative and zero conjugation curvature, as introduced by Bar-Natan et al. (JTA, 2020,
https://doi.org/10.1142/S1793525321500096
). |
| doi_str_mv | 10.1007/s10711-022-00683-w |
| format | Article |
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BS
(1,
n
) and show that the growth rate of this language is the growth rate of the group. This provides a straightforward calculation of the growth rate of
BS
(1,
n
), which was initially computed by Collins et al. (AM (Basel) 62:1-11, 1994). Our methods are based on those we develop in Taback and Walker (JTA, to appear) to show that
BS
(1,
n
) has a positive density of elements of positive, negative and zero conjugation curvature, as introduced by Bar-Natan et al. (JTA, 2020,
https://doi.org/10.1142/S1793525321500096
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BS
(1,
n
) and show that the growth rate of this language is the growth rate of the group. This provides a straightforward calculation of the growth rate of
BS
(1,
n
), which was initially computed by Collins et al. (AM (Basel) 62:1-11, 1994). Our methods are based on those we develop in Taback and Walker (JTA, to appear) to show that
BS
(1,
n
) has a positive density of elements of positive, negative and zero conjugation curvature, as introduced by Bar-Natan et al. (JTA, 2020,
https://doi.org/10.1142/S1793525321500096
).</description><subject>Algebraic Geometry</subject><subject>Conjugation</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Geodesy</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>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kM9Kw0AQxhdRsFZfwFPA8-rsbJLNHmtRKxQ8qOdl20z6h7RbdxODN9_BN_RJ3BrFmzAwMPy-b2Y-xs4FXAoAdRUEKCE4IHKAvJC8O2ADkSnkWuTFIRsApDnPVJYds5MQ1gCglcIBm4ySLXXJzjtXJbGaJSUL77pmmXjb0O8ouPrVzmpKrm27CbVdfL5_PLp61Vi_x9tdOGVHla0Dnf30IXu-vXkaT_j04e5-PJryOSpouMwLpWdliplKS5SVFhJLRdKKUltBpURbCFJVKrXAeWHzWRV5qYmwoLSUcsguet948ktLoTFr1_ptXGkwlypTOr4fKeypuXcheKrMzq821r8ZAWafmOkTMzEx852Y6aJI9qIQ4e2C_J_1P6ovgJhvCA</recordid><startdate>20220401</startdate><enddate>20220401</enddate><creator>Taback, Jennifer</creator><creator>Walker, Alden</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3854-8624</orcidid></search><sort><creationdate>20220401</creationdate><title>A new proof of the growth rate of the solvable Baumslag–Solitar groups</title><author>Taback, Jennifer ; Walker, Alden</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-36879bd42574d23f9132d7e3a1d9a1ed32a81e7f43912c8a6bf79b39ee28e4d33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algebraic Geometry</topic><topic>Conjugation</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Geodesy</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>Taback, Jennifer</creatorcontrib><creatorcontrib>Walker, Alden</creatorcontrib><collection>CrossRef</collection><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Taback, Jennifer</au><au>Walker, Alden</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new proof of the growth rate of the solvable Baumslag–Solitar groups</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2022-04-01</date><risdate>2022</risdate><volume>216</volume><issue>2</issue><artnum>22</artnum><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>We exhibit a regular language of geodesics for a large set of elements of
BS
(1,
n
) and show that the growth rate of this language is the growth rate of the group. This provides a straightforward calculation of the growth rate of
BS
(1,
n
), which was initially computed by Collins et al. (AM (Basel) 62:1-11, 1994). Our methods are based on those we develop in Taback and Walker (JTA, to appear) to show that
BS
(1,
n
) has a positive density of elements of positive, negative and zero conjugation curvature, as introduced by Bar-Natan et al. (JTA, 2020,
https://doi.org/10.1142/S1793525321500096
).</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-022-00683-w</doi><orcidid>https://orcid.org/0000-0002-3854-8624</orcidid></addata></record> |
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| issn | 0046-5755 1572-9168 |
| language | eng |
| recordid | cdi_proquest_journals_2637579683 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebraic Geometry Conjugation Convex and Discrete Geometry Differential Geometry Geodesy Hyperbolic Geometry Mathematics Mathematics and Statistics Original Paper Projective Geometry Topology |
| title | A new proof of the growth rate of the solvable Baumslag–Solitar groups |
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