A note on the combinatorial structure of finite and locally finite simplicial complexes of nonpositive curvature
We investigate the collapsibility of systolic finite simplicial complexes of arbitrary dimension. The main tool we use in the proof is discrete Morse theory. We shall consider a convex subcomplex of the complex and project any simplex of the complex onto a ball around this convex subcomplex. These p...
Gespeichert in:
| Veröffentlicht in: | Bulletin mathématiques de la Société des sciences mathématiques de Roumanie 2016-01, Vol.59(107) (3), p.205-216 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 216 |
|---|---|
| container_issue | 3 |
| container_start_page | 205 |
| container_title | Bulletin mathématiques de la Société des sciences mathématiques de Roumanie |
| container_volume | 59(107) |
| creator | Baraliç, Djordje Lazăr, Ioana-Claudia |
| description | We investigate the collapsibility of systolic finite simplicial complexes of arbitrary dimension. The main tool we use in the proof is discrete Morse theory. We shall consider a convex subcomplex of the complex and project any simplex of the complex onto a ball around this convex subcomplex. These projections will induce a convenient gradient matching on the complex. Besides we analyze the combinatorial structure of both CAT(0) and systolic locally finite simplicial complexes of arbitrary dimensions. We will show that both such complexes possess an arborescent structure. Along the way we make use of certain well known results regarding systolic geometry. |
| format | Article |
| fullrecord | <record><control><sourceid>jstor</sourceid><recordid>TN_cdi_jstor_primary_26423355</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>26423355</jstor_id><sourcerecordid>26423355</sourcerecordid><originalsourceid>FETCH-LOGICAL-j177t-ad7b7928da8145759f3b65e7b61aa71e395a58bdf7bd00dc842a30ba747c4a33</originalsourceid><addsrcrecordid>eNo1kMtqwzAQRUVpoSbNJxT0AwY9PfYyhL4g0E32YWTLVEaWjCWH5u9r03Y1MHfOgTt3pBCs0iUTlbonBReClbIG9Uj2KQ2MMc5AKICCTAcaYrY0Bpq_LG3jaFzAHGeHnqY8L21e5jXuae-CWw8xdNTHFr2__a-SGyfv2o1Y-cnbb5s2IsQwxeSyu67iZb7ipnoiDz36ZPd_c0fOry_n43t5-nz7OB5O5cABcokdGGhE3WHNlQbd9NJU2oKpOCJwKxuNujZdD6ZjrGtrJVAyg6CgVSjljjz_aoe0lrlMsxtxvl3WfwgptZY_HYZXYw</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A note on the combinatorial structure of finite and locally finite simplicial complexes of nonpositive curvature</title><source>JSTOR Mathematics & Statistics</source><source>Alma/SFX Local Collection</source><creator>Baraliç, Djordje ; Lazăr, Ioana-Claudia</creator><creatorcontrib>Baraliç, Djordje ; Lazăr, Ioana-Claudia</creatorcontrib><description>We investigate the collapsibility of systolic finite simplicial complexes of arbitrary dimension. The main tool we use in the proof is discrete Morse theory. We shall consider a convex subcomplex of the complex and project any simplex of the complex onto a ball around this convex subcomplex. These projections will induce a convenient gradient matching on the complex. Besides we analyze the combinatorial structure of both CAT(0) and systolic locally finite simplicial complexes of arbitrary dimensions. We will show that both such complexes possess an arborescent structure. Along the way we make use of certain well known results regarding systolic geometry.</description><identifier>ISSN: 1220-3874</identifier><identifier>EISSN: 2065-0264</identifier><language>eng</language><publisher>SOCIETATEA DE ŞTIINŢE MATEMATICE DIN ROMÂNIA</publisher><ispartof>Bulletin mathématiques de la Société des sciences mathématiques de Roumanie, 2016-01, Vol.59(107) (3), p.205-216</ispartof><rights>Copyright © 2016 SSMR</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/26423355$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/26423355$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,828,57999,58232</link.rule.ids></links><search><creatorcontrib>Baraliç, Djordje</creatorcontrib><creatorcontrib>Lazăr, Ioana-Claudia</creatorcontrib><title>A note on the combinatorial structure of finite and locally finite simplicial complexes of nonpositive curvature</title><title>Bulletin mathématiques de la Société des sciences mathématiques de Roumanie</title><description>We investigate the collapsibility of systolic finite simplicial complexes of arbitrary dimension. The main tool we use in the proof is discrete Morse theory. We shall consider a convex subcomplex of the complex and project any simplex of the complex onto a ball around this convex subcomplex. These projections will induce a convenient gradient matching on the complex. Besides we analyze the combinatorial structure of both CAT(0) and systolic locally finite simplicial complexes of arbitrary dimensions. We will show that both such complexes possess an arborescent structure. Along the way we make use of certain well known results regarding systolic geometry.</description><issn>1220-3874</issn><issn>2065-0264</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNo1kMtqwzAQRUVpoSbNJxT0AwY9PfYyhL4g0E32YWTLVEaWjCWH5u9r03Y1MHfOgTt3pBCs0iUTlbonBReClbIG9Uj2KQ2MMc5AKICCTAcaYrY0Bpq_LG3jaFzAHGeHnqY8L21e5jXuae-CWw8xdNTHFr2__a-SGyfv2o1Y-cnbb5s2IsQwxeSyu67iZb7ipnoiDz36ZPd_c0fOry_n43t5-nz7OB5O5cABcokdGGhE3WHNlQbd9NJU2oKpOCJwKxuNujZdD6ZjrGtrJVAyg6CgVSjljjz_aoe0lrlMsxtxvl3WfwgptZY_HYZXYw</recordid><startdate>20160101</startdate><enddate>20160101</enddate><creator>Baraliç, Djordje</creator><creator>Lazăr, Ioana-Claudia</creator><general>SOCIETATEA DE ŞTIINŢE MATEMATICE DIN ROMÂNIA</general><scope/></search><sort><creationdate>20160101</creationdate><title>A note on the combinatorial structure of finite and locally finite simplicial complexes of nonpositive curvature</title><author>Baraliç, Djordje ; Lazăr, Ioana-Claudia</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-j177t-ad7b7928da8145759f3b65e7b61aa71e395a58bdf7bd00dc842a30ba747c4a33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><toplevel>online_resources</toplevel><creatorcontrib>Baraliç, Djordje</creatorcontrib><creatorcontrib>Lazăr, Ioana-Claudia</creatorcontrib><jtitle>Bulletin mathématiques de la Société des sciences mathématiques de Roumanie</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Baraliç, Djordje</au><au>Lazăr, Ioana-Claudia</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A note on the combinatorial structure of finite and locally finite simplicial complexes of nonpositive curvature</atitle><jtitle>Bulletin mathématiques de la Société des sciences mathématiques de Roumanie</jtitle><date>2016-01-01</date><risdate>2016</risdate><volume>59(107)</volume><issue>3</issue><spage>205</spage><epage>216</epage><pages>205-216</pages><issn>1220-3874</issn><eissn>2065-0264</eissn><abstract>We investigate the collapsibility of systolic finite simplicial complexes of arbitrary dimension. The main tool we use in the proof is discrete Morse theory. We shall consider a convex subcomplex of the complex and project any simplex of the complex onto a ball around this convex subcomplex. These projections will induce a convenient gradient matching on the complex. Besides we analyze the combinatorial structure of both CAT(0) and systolic locally finite simplicial complexes of arbitrary dimensions. We will show that both such complexes possess an arborescent structure. Along the way we make use of certain well known results regarding systolic geometry.</abstract><pub>SOCIETATEA DE ŞTIINŢE MATEMATICE DIN ROMÂNIA</pub><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1220-3874 |
| ispartof | Bulletin mathématiques de la Société des sciences mathématiques de Roumanie, 2016-01, Vol.59(107) (3), p.205-216 |
| issn | 1220-3874 2065-0264 |
| language | eng |
| recordid | cdi_jstor_primary_26423355 |
| source | JSTOR Mathematics & Statistics; Alma/SFX Local Collection |
| title | A note on the combinatorial structure of finite and locally finite simplicial complexes of nonpositive curvature |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-25T16%3A15%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20note%20on%20the%20combinatorial%20structure%20of%20finite%20and%20locally%20finite%20simplicial%20complexes%20of%20nonpositive%20curvature&rft.jtitle=Bulletin%20math%C3%A9matiques%20de%20la%20Soci%C3%A9t%C3%A9%20des%20sciences%20math%C3%A9matiques%20de%20Roumanie&rft.au=Barali%C3%A7,%20Djordje&rft.date=2016-01-01&rft.volume=59(107)&rft.issue=3&rft.spage=205&rft.epage=216&rft.pages=205-216&rft.issn=1220-3874&rft.eissn=2065-0264&rft_id=info:doi/&rft_dat=%3Cjstor%3E26423355%3C/jstor%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=26423355&rfr_iscdi=true |