Invariants and TQFT's for cut cellular surfaces from finite 2-groups
Boletim da Sociedade Portuguesa de Matem\'atica 76, 159-176 (2018) In this brief sequel to a previous article, we recall the notion of a cut cellular surface (CCS), being a surface with boundary, which is cut in a specified way to be represented in the plane, and is composed of 0-, 1- and 2-cel...
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| creator | Bragança, Diogo Picken, Roger |
| description | Boletim da Sociedade Portuguesa de Matem\'atica 76, 159-176 (2018) In this brief sequel to a previous article, we recall the notion of a cut
cellular surface (CCS), being a surface with boundary, which is cut in a
specified way to be represented in the plane, and is composed of 0-, 1- and
2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular
structure, by counting colourings of the 1- and 2-cells with elements of a
finite 2-group, subject to a "fake flatness" condition for each 2-cell. These
invariants, which extend Yetter's invariants to this class of surfaces, are
also described in a TQFT setting. A result from the previous article concerning
the commuting fraction of a group is generalized to the 2-group context. |
| doi_str_mv | 10.48550/arxiv.1710.02390 |
| format | Article |
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cellular surface (CCS), being a surface with boundary, which is cut in a
specified way to be represented in the plane, and is composed of 0-, 1- and
2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular
structure, by counting colourings of the 1- and 2-cells with elements of a
finite 2-group, subject to a "fake flatness" condition for each 2-cell. These
invariants, which extend Yetter's invariants to this class of surfaces, are
also described in a TQFT setting. A result from the previous article concerning
the commuting fraction of a group is generalized to the 2-group context.</description><identifier>DOI: 10.48550/arxiv.1710.02390</identifier><language>eng</language><subject>Mathematics - Geometric Topology</subject><creationdate>2017-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1710.02390$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1710.02390$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Bragança, Diogo</creatorcontrib><creatorcontrib>Picken, Roger</creatorcontrib><title>Invariants and TQFT's for cut cellular surfaces from finite 2-groups</title><description>Boletim da Sociedade Portuguesa de Matem\'atica 76, 159-176 (2018) In this brief sequel to a previous article, we recall the notion of a cut
cellular surface (CCS), being a surface with boundary, which is cut in a
specified way to be represented in the plane, and is composed of 0-, 1- and
2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular
structure, by counting colourings of the 1- and 2-cells with elements of a
finite 2-group, subject to a "fake flatness" condition for each 2-cell. These
invariants, which extend Yetter's invariants to this class of surfaces, are
also described in a TQFT setting. A result from the previous article concerning
the commuting fraction of a group is generalized to the 2-group context.</description><subject>Mathematics - Geometric Topology</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzNAcKGBgZWxpwMrh45pUlFmUm5pUUKyTmpSiEBLqFqBcrpOUXKSSXligkp-bklOYkFikUlxalJSanAmWK8nMV0jLzMktSFYx004vySwuKeRhY0xJzilN5oTQ3g7yba4izhy7YvviCoszcxKLKeJC98WB7jQmrAACa8Dd9</recordid><startdate>20171004</startdate><enddate>20171004</enddate><creator>Bragança, Diogo</creator><creator>Picken, Roger</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20171004</creationdate><title>Invariants and TQFT's for cut cellular surfaces from finite 2-groups</title><author>Bragança, Diogo ; Picken, Roger</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_1710_023903</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics - Geometric Topology</topic><toplevel>online_resources</toplevel><creatorcontrib>Bragança, Diogo</creatorcontrib><creatorcontrib>Picken, Roger</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bragança, Diogo</au><au>Picken, Roger</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Invariants and TQFT's for cut cellular surfaces from finite 2-groups</atitle><date>2017-10-04</date><risdate>2017</risdate><abstract>Boletim da Sociedade Portuguesa de Matem\'atica 76, 159-176 (2018) In this brief sequel to a previous article, we recall the notion of a cut
cellular surface (CCS), being a surface with boundary, which is cut in a
specified way to be represented in the plane, and is composed of 0-, 1- and
2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular
structure, by counting colourings of the 1- and 2-cells with elements of a
finite 2-group, subject to a "fake flatness" condition for each 2-cell. These
invariants, which extend Yetter's invariants to this class of surfaces, are
also described in a TQFT setting. A result from the previous article concerning
the commuting fraction of a group is generalized to the 2-group context.</abstract><doi>10.48550/arxiv.1710.02390</doi><oa>free_for_read</oa></addata></record> |
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| title | Invariants and TQFT's for cut cellular surfaces from finite 2-groups |
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