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Exceptional surgery and boundary slopes
Let X be a norm curve in the \mathit{SL}(2,\mathbb{C})-character variety of a knot exterior M. Let t = \|\beta\| / \|\alpha\| be the ratio of the Culler-Shalen norms of two distinct non-zero classes \alpha, \beta \in H_1(\partial M,\mathbb{Z}). We demonstrate that either X has exactly two associated...
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| Published in: | Osaka journal of mathematics 2006-12, Vol.43 (no. 4), p.807-821 |
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| Main Authors: | , , |
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| Language: | English |
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| container_end_page | 821 |
| container_issue | no. 4 |
| container_start_page | 807 |
| container_title | Osaka journal of mathematics |
| container_volume | 43 |
| creator | Ishikawa, Masaharu Mattman, Thomas W Shimokawa, Koya |
| description | Let X be a norm curve in the \mathit{SL}(2,\mathbb{C})-character
variety of a knot exterior M. Let t = \|\beta\| / \|\alpha\|
be the ratio of the Culler-Shalen norms of two distinct non-zero
classes \alpha, \beta \in H_1(\partial M,\mathbb{Z}). We
demonstrate that either X has exactly two associated strict
boundary slopes \pm t, or else there are strict boundary
slopes r_1 and r_2 with |r_1| > t and |r_2| <
t. As a consequence, we show that there are strict boundary
slopes near cyclic, finite, and Seifert slopes. We also prove
that the diameter of the set of strict boundary slopes can
be bounded below using the Culler-Shalen norm of those slopes. |
| format | article |
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variety of a knot exterior M. Let t = \|\beta\| / \|\alpha\|
be the ratio of the Culler-Shalen norms of two distinct non-zero
classes \alpha, \beta \in H_1(\partial M,\mathbb{Z}). We
demonstrate that either X has exactly two associated strict
boundary slopes \pm t, or else there are strict boundary
slopes r_1 and r_2 with |r_1| > t and |r_2| <
t. As a consequence, we show that there are strict boundary
slopes near cyclic, finite, and Seifert slopes. We also prove
that the diameter of the set of strict boundary slopes can
be bounded below using the Culler-Shalen norm of those slopes.</description><language>eng</language><publisher>Osaka University and Osaka City University, Departments of Mathematics</publisher><subject>57M25 ; 57N10</subject><ispartof>Osaka journal of mathematics, 2006-12, Vol.43 (no. 4), p.807-821</ispartof><rights>Copyright 2006 Osaka University and Osaka City University, Departments of Mathematics</rights><lds50>peer_reviewed</lds50><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>230,314,780,784,882,885</link.rule.ids></links><search><creatorcontrib>Ishikawa, Masaharu</creatorcontrib><creatorcontrib>Mattman, Thomas W</creatorcontrib><creatorcontrib>Shimokawa, Koya</creatorcontrib><title>Exceptional surgery and boundary slopes</title><title>Osaka journal of mathematics</title><description>Let X be a norm curve in the \mathit{SL}(2,\mathbb{C})-character
variety of a knot exterior M. Let t = \|\beta\| / \|\alpha\|
be the ratio of the Culler-Shalen norms of two distinct non-zero
classes \alpha, \beta \in H_1(\partial M,\mathbb{Z}). We
demonstrate that either X has exactly two associated strict
boundary slopes \pm t, or else there are strict boundary
slopes r_1 and r_2 with |r_1| > t and |r_2| <
t. As a consequence, we show that there are strict boundary
slopes near cyclic, finite, and Seifert slopes. We also prove
that the diameter of the set of strict boundary slopes can
be bounded below using the Culler-Shalen norm of those slopes.</description><subject>57M25</subject><subject>57N10</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNotjktrg0AURmcTSJvkP7jLSpiH89qlSNoGhGyStVy916IYRxyF9N83UFeH7yw-zpa9x9hxnhlr-Rs7np81jXMbBuiTuEw_NP0mMGBShWVAeI3Yh5Hinm0a6CMdVu7Y_fN8y7_T4vp1yT-KdJBOz6nOuBOelPLOK6GzphFQucw7DRpRGRSWKukRpJeN8bL2yJ3htkKyGlCoHTv9_45T6Kieaan7Fstxah-vmDJAW-b3YrUrQvcohTDaac6VVX-gUESQ</recordid><startdate>20061201</startdate><enddate>20061201</enddate><creator>Ishikawa, Masaharu</creator><creator>Mattman, Thomas W</creator><creator>Shimokawa, Koya</creator><general>Osaka University and Osaka City University, Departments of Mathematics</general><scope/></search><sort><creationdate>20061201</creationdate><title>Exceptional surgery and boundary slopes</title><author>Ishikawa, Masaharu ; Mattman, Thomas W ; Shimokawa, Koya</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-n285t-540819e339893154ff1ab84985a5dd36d17eb29da292f692c9d08607bde75ad13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>57M25</topic><topic>57N10</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ishikawa, Masaharu</creatorcontrib><creatorcontrib>Mattman, Thomas W</creatorcontrib><creatorcontrib>Shimokawa, Koya</creatorcontrib><jtitle>Osaka journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ishikawa, Masaharu</au><au>Mattman, Thomas W</au><au>Shimokawa, Koya</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exceptional surgery and boundary slopes</atitle><jtitle>Osaka journal of mathematics</jtitle><date>2006-12-01</date><risdate>2006</risdate><volume>43</volume><issue>no. 4</issue><spage>807</spage><epage>821</epage><pages>807-821</pages><abstract>Let X be a norm curve in the \mathit{SL}(2,\mathbb{C})-character
variety of a knot exterior M. Let t = \|\beta\| / \|\alpha\|
be the ratio of the Culler-Shalen norms of two distinct non-zero
classes \alpha, \beta \in H_1(\partial M,\mathbb{Z}). We
demonstrate that either X has exactly two associated strict
boundary slopes \pm t, or else there are strict boundary
slopes r_1 and r_2 with |r_1| > t and |r_2| <
t. As a consequence, we show that there are strict boundary
slopes near cyclic, finite, and Seifert slopes. We also prove
that the diameter of the set of strict boundary slopes can
be bounded below using the Culler-Shalen norm of those slopes.</abstract><pub>Osaka University and Osaka City University, Departments of Mathematics</pub><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Osaka journal of mathematics, 2006-12, Vol.43 (no. 4), p.807-821 |
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| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_ojm_1165850037 |
| source | Project Euclid Open Access |
| subjects | 57M25 57N10 |
| title | Exceptional surgery and boundary slopes |
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