Free groups generated by two screw parabolic maps
In this paper, we provide sufficient conditions for groups generated by two screw parabolic maps of PU ( 2 , 1 ) with distinct fixed points to be discrete and free. As an example, we apply our results to the classical group ⟨ g θ , f θ ⟩ constructed in Gusevskii, N., Parker, J.R.: Representations of...
Gespeichert in:
| Veröffentlicht in: | Geometriae dedicata 2024-12, Vol.218 (6), Article 107 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 6 |
| container_start_page | |
| container_title | Geometriae dedicata |
| container_volume | 218 |
| creator | Liao, Wei Xie, Baohua |
| description | In this paper, we provide sufficient conditions for groups generated by two screw parabolic maps of
PU
(
2
,
1
)
with distinct fixed points to be discrete and free. As an example, we apply our results to the classical group
⟨
g
θ
,
f
θ
⟩
constructed in Gusevskii, N., Parker, J.R.: Representations of free Fuchsian groups in complex hyperbolic space. Topology 39, 33–60 (2000). |
| doi_str_mv | 10.1007/s10711-024-00958-4 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3116658639</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3116658639</sourcerecordid><originalsourceid>FETCH-LOGICAL-c200t-772174b5b876dfbe2763d7a898f83503c1c38773f188997438333fb97b108d9d3</originalsourceid><addsrcrecordid>eNp9kEFLAzEQRoMoWKt_wFPAc3Rms8kkRylWhYIXPYfsbra0tN012aX03xtdwZunubzvDTzGbhHuEYAeEgIhCihKAWCVEeUZm6GiQljU5pzNAEotFCl1ya5S2kKmiIoZw2UMga9jN_aJr8MhRD-EhlcnPhw7nuoYjrz30VfdblPzve_TNbto_S6Fm987Zx_Lp_fFi1i9Pb8uHleiLgAGke1IZaUqQ7ppq1CQlg15Y01rpAJZYy0NkWzRGGuplEZK2VaWKgTT2EbO2d3k7WP3OYY0uG03xkN-6SSi1spoaTNVTFQdu5RiaF0fN3sfTw7BfadxUxqX07ifNK7MIzmNUoYP6xD_1P-svgB5OmQd</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3116658639</pqid></control><display><type>article</type><title>Free groups generated by two screw parabolic maps</title><source>Springer Nature - Complete Springer Journals</source><creator>Liao, Wei ; Xie, Baohua</creator><creatorcontrib>Liao, Wei ; Xie, Baohua</creatorcontrib><description>In this paper, we provide sufficient conditions for groups generated by two screw parabolic maps of
PU
(
2
,
1
)
with distinct fixed points to be discrete and free. As an example, we apply our results to the classical group
⟨
g
θ
,
f
θ
⟩
constructed in Gusevskii, N., Parker, J.R.: Representations of free Fuchsian groups in complex hyperbolic space. Topology 39, 33–60 (2000).</description><identifier>ISSN: 0046-5755</identifier><identifier>EISSN: 1572-9168</identifier><identifier>DOI: 10.1007/s10711-024-00958-4</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebraic Geometry ; Convex and Discrete Geometry ; Differential Geometry ; Hyperbolic coordinates ; Hyperbolic Geometry ; Mathematics ; Mathematics and Statistics ; Original Paper ; Projective Geometry ; Topology</subject><ispartof>Geometriae dedicata, 2024-12, Vol.218 (6), Article 107</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-772174b5b876dfbe2763d7a898f83503c1c38773f188997438333fb97b108d9d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10711-024-00958-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10711-024-00958-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Liao, Wei</creatorcontrib><creatorcontrib>Xie, Baohua</creatorcontrib><title>Free groups generated by two screw parabolic maps</title><title>Geometriae dedicata</title><addtitle>Geom Dedicata</addtitle><description>In this paper, we provide sufficient conditions for groups generated by two screw parabolic maps of
PU
(
2
,
1
)
with distinct fixed points to be discrete and free. As an example, we apply our results to the classical group
⟨
g
θ
,
f
θ
⟩
constructed in Gusevskii, N., Parker, J.R.: Representations of free Fuchsian groups in complex hyperbolic space. Topology 39, 33–60 (2000).</description><subject>Algebraic Geometry</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Hyperbolic coordinates</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>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLAzEQRoMoWKt_wFPAc3Rms8kkRylWhYIXPYfsbra0tN012aX03xtdwZunubzvDTzGbhHuEYAeEgIhCihKAWCVEeUZm6GiQljU5pzNAEotFCl1ya5S2kKmiIoZw2UMga9jN_aJr8MhRD-EhlcnPhw7nuoYjrz30VfdblPzve_TNbto_S6Fm987Zx_Lp_fFi1i9Pb8uHleiLgAGke1IZaUqQ7ppq1CQlg15Y01rpAJZYy0NkWzRGGuplEZK2VaWKgTT2EbO2d3k7WP3OYY0uG03xkN-6SSi1spoaTNVTFQdu5RiaF0fN3sfTw7BfadxUxqX07ifNK7MIzmNUoYP6xD_1P-svgB5OmQd</recordid><startdate>20241201</startdate><enddate>20241201</enddate><creator>Liao, Wei</creator><creator>Xie, Baohua</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20241201</creationdate><title>Free groups generated by two screw parabolic maps</title><author>Liao, Wei ; Xie, Baohua</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-772174b5b876dfbe2763d7a898f83503c1c38773f188997438333fb97b108d9d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algebraic Geometry</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Hyperbolic coordinates</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>Liao, Wei</creatorcontrib><creatorcontrib>Xie, Baohua</creatorcontrib><collection>CrossRef</collection><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liao, Wei</au><au>Xie, Baohua</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Free groups generated by two screw parabolic maps</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2024-12-01</date><risdate>2024</risdate><volume>218</volume><issue>6</issue><artnum>107</artnum><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>In this paper, we provide sufficient conditions for groups generated by two screw parabolic maps of
PU
(
2
,
1
)
with distinct fixed points to be discrete and free. As an example, we apply our results to the classical group
⟨
g
θ
,
f
θ
⟩
constructed in Gusevskii, N., Parker, J.R.: Representations of free Fuchsian groups in complex hyperbolic space. Topology 39, 33–60 (2000).</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-024-00958-4</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0046-5755 |
| ispartof | Geometriae dedicata, 2024-12, Vol.218 (6), Article 107 |
| issn | 0046-5755 1572-9168 |
| language | eng |
| recordid | cdi_proquest_journals_3116658639 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebraic Geometry Convex and Discrete Geometry Differential Geometry Hyperbolic coordinates Hyperbolic Geometry Mathematics Mathematics and Statistics Original Paper Projective Geometry Topology |
| title | Free groups generated by two screw parabolic maps |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-02T15%3A55%3A07IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Free%20groups%20generated%20by%20two%20screw%20parabolic%20maps&rft.jtitle=Geometriae%20dedicata&rft.au=Liao,%20Wei&rft.date=2024-12-01&rft.volume=218&rft.issue=6&rft.artnum=107&rft.issn=0046-5755&rft.eissn=1572-9168&rft_id=info:doi/10.1007/s10711-024-00958-4&rft_dat=%3Cproquest_cross%3E3116658639%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3116658639&rft_id=info:pmid/&rfr_iscdi=true |