Higher Homotopy Commutativity of H-Spaces and the Permuto-Associahedra
In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an $A_n-space$. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected $A_p-space$ has the finitely gen...
Gespeichert in:
| Veröffentlicht in: | Transactions of the American Mathematical Society 2004-10, Vol.356 (10), p.3823-3839 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 3839 |
|---|---|
| container_issue | 10 |
| container_start_page | 3823 |
| container_title | Transactions of the American Mathematical Society |
| container_volume | 356 |
| creator | Hemmi, Yutaka Kawamoto, Yusuke |
| description | In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an $A_n-space$. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected $A_p-space$ has the finitely generated mod p cohomology for a prime p and the multiplication of it is homotopy commutative of the p-th order, then it has the mod p homotopy type of a finite product of Eilenberg-Mac Lane spaces K(Z, 1)s, K(Z, 2)s and $K(Z/p^i, 1)s$ for i ≥ 1. |
| doi_str_mv | 10.1090/S0002-9947-04-03647-5 |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_pasca</sourceid><recordid>TN_cdi_pascalfrancis_primary_16171772</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>3844962</jstor_id><sourcerecordid>3844962</sourcerecordid><originalsourceid>FETCH-LOGICAL-j248t-6414749ef243d89d765c4a33211a76624faccea3a7150769b6455141e81dca593</originalsourceid><addsrcrecordid>eNo9zEtLAzEUBeAgCtbqP1CYjctoHjevZSm2IxQUqutyzWTslE4zJFHov3eg0tU9h_NxCXng7Ikzx57XjDFBnQNDGVAm9RjUBZlwZi3VVrFLMjmTa3KT826sDKyekEXdfW9DqurYxxKHYzWPff9TsHS_XTlWsa1quh7Qh1zhoanKNlTvIY0i0lnO0Xe4DU3CW3LV4j6Hu_87JZ-Ll495TVdvy9f5bEV3AmyhGjgYcKEVIBvrGqOVB5RScI5GawEteh9QouGKGe2-NCjFgQfLG4_KySl5PP0dMHvctwkPvsubIXU9puOGa264MWJ09ye3yyWm8y4tgNNC_gFXAFee</addsrcrecordid><sourcetype>Index Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Higher Homotopy Commutativity of H-Spaces and the Permuto-Associahedra</title><source>Jstor Complete Legacy</source><source>American Mathematical Society Publications</source><source>American Mathematical Society Publications (Freely Accessible)</source><source>EZB-FREE-00999 freely available EZB journals</source><source>JSTOR Mathematics & Statistics</source><creator>Hemmi, Yutaka ; Kawamoto, Yusuke</creator><creatorcontrib>Hemmi, Yutaka ; Kawamoto, Yusuke</creatorcontrib><description>In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an $A_n-space$. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected $A_p-space$ has the finitely generated mod p cohomology for a prime p and the multiplication of it is homotopy commutative of the p-th order, then it has the mod p homotopy type of a finite product of Eilenberg-Mac Lane spaces K(Z, 1)s, K(Z, 2)s and $K(Z/p^i, 1)s$ for i ≥ 1.</description><identifier>ISSN: 0002-9947</identifier><identifier>EISSN: 1088-6850</identifier><identifier>DOI: 10.1090/S0002-9947-04-03647-5</identifier><identifier>CODEN: TAMTAM</identifier><language>eng</language><publisher>Providence, RI: American Mathematical Society</publisher><subject>Algebra ; Algebraic topology ; Commutativity ; Convex and discrete geometry ; Exact sciences and technology ; Geometry ; Hexagons ; Lie groups ; Mathematical theorems ; Mathematics ; Polyhedrons ; Sciences and techniques of general use ; Topological theorems ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds ; Vertices</subject><ispartof>Transactions of the American Mathematical Society, 2004-10, Vol.356 (10), p.3823-3839</ispartof><rights>Copyright 2004 American Mathematical Society</rights><rights>2004 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/3844962$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/3844962$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,27901,27902,57992,57996,58225,58229</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16171772$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Hemmi, Yutaka</creatorcontrib><creatorcontrib>Kawamoto, Yusuke</creatorcontrib><title>Higher Homotopy Commutativity of H-Spaces and the Permuto-Associahedra</title><title>Transactions of the American Mathematical Society</title><description>In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an $A_n-space$. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected $A_p-space$ has the finitely generated mod p cohomology for a prime p and the multiplication of it is homotopy commutative of the p-th order, then it has the mod p homotopy type of a finite product of Eilenberg-Mac Lane spaces K(Z, 1)s, K(Z, 2)s and $K(Z/p^i, 1)s$ for i ≥ 1.</description><subject>Algebra</subject><subject>Algebraic topology</subject><subject>Commutativity</subject><subject>Convex and discrete geometry</subject><subject>Exact sciences and technology</subject><subject>Geometry</subject><subject>Hexagons</subject><subject>Lie groups</subject><subject>Mathematical theorems</subject><subject>Mathematics</subject><subject>Polyhedrons</subject><subject>Sciences and techniques of general use</subject><subject>Topological theorems</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><subject>Vertices</subject><issn>0002-9947</issn><issn>1088-6850</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><recordid>eNo9zEtLAzEUBeAgCtbqP1CYjctoHjevZSm2IxQUqutyzWTslE4zJFHov3eg0tU9h_NxCXng7Ikzx57XjDFBnQNDGVAm9RjUBZlwZi3VVrFLMjmTa3KT826sDKyekEXdfW9DqurYxxKHYzWPff9TsHS_XTlWsa1quh7Qh1zhoanKNlTvIY0i0lnO0Xe4DU3CW3LV4j6Hu_87JZ-Ll495TVdvy9f5bEV3AmyhGjgYcKEVIBvrGqOVB5RScI5GawEteh9QouGKGe2-NCjFgQfLG4_KySl5PP0dMHvctwkPvsubIXU9puOGa264MWJ09ye3yyWm8y4tgNNC_gFXAFee</recordid><startdate>200410</startdate><enddate>200410</enddate><creator>Hemmi, Yutaka</creator><creator>Kawamoto, Yusuke</creator><general>American Mathematical Society</general><scope>IQODW</scope></search><sort><creationdate>200410</creationdate><title>Higher Homotopy Commutativity of H-Spaces and the Permuto-Associahedra</title><author>Hemmi, Yutaka ; Kawamoto, Yusuke</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-j248t-6414749ef243d89d765c4a33211a76624faccea3a7150769b6455141e81dca593</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Algebra</topic><topic>Algebraic topology</topic><topic>Commutativity</topic><topic>Convex and discrete geometry</topic><topic>Exact sciences and technology</topic><topic>Geometry</topic><topic>Hexagons</topic><topic>Lie groups</topic><topic>Mathematical theorems</topic><topic>Mathematics</topic><topic>Polyhedrons</topic><topic>Sciences and techniques of general use</topic><topic>Topological theorems</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><topic>Vertices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hemmi, Yutaka</creatorcontrib><creatorcontrib>Kawamoto, Yusuke</creatorcontrib><collection>Pascal-Francis</collection><jtitle>Transactions of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hemmi, Yutaka</au><au>Kawamoto, Yusuke</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Higher Homotopy Commutativity of H-Spaces and the Permuto-Associahedra</atitle><jtitle>Transactions of the American Mathematical Society</jtitle><date>2004-10</date><risdate>2004</risdate><volume>356</volume><issue>10</issue><spage>3823</spage><epage>3839</epage><pages>3823-3839</pages><issn>0002-9947</issn><eissn>1088-6850</eissn><coden>TAMTAM</coden><abstract>In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an $A_n-space$. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected $A_p-space$ has the finitely generated mod p cohomology for a prime p and the multiplication of it is homotopy commutative of the p-th order, then it has the mod p homotopy type of a finite product of Eilenberg-Mac Lane spaces K(Z, 1)s, K(Z, 2)s and $K(Z/p^i, 1)s$ for i ≥ 1.</abstract><cop>Providence, RI</cop><pub>American Mathematical Society</pub><doi>10.1090/S0002-9947-04-03647-5</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0002-9947 |
| ispartof | Transactions of the American Mathematical Society, 2004-10, Vol.356 (10), p.3823-3839 |
| issn | 0002-9947 1088-6850 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_16171772 |
| source | Jstor Complete Legacy; American Mathematical Society Publications; American Mathematical Society Publications (Freely Accessible); EZB-FREE-00999 freely available EZB journals; JSTOR Mathematics & Statistics |
| subjects | Algebra Algebraic topology Commutativity Convex and discrete geometry Exact sciences and technology Geometry Hexagons Lie groups Mathematical theorems Mathematics Polyhedrons Sciences and techniques of general use Topological theorems Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Vertices |
| title | Higher Homotopy Commutativity of H-Spaces and the Permuto-Associahedra |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-04T22%3A12%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_pasca&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Higher%20Homotopy%20Commutativity%20of%20H-Spaces%20and%20the%20Permuto-Associahedra&rft.jtitle=Transactions%20of%20the%20American%20Mathematical%20Society&rft.au=Hemmi,%20Yutaka&rft.date=2004-10&rft.volume=356&rft.issue=10&rft.spage=3823&rft.epage=3839&rft.pages=3823-3839&rft.issn=0002-9947&rft.eissn=1088-6850&rft.coden=TAMTAM&rft_id=info:doi/10.1090/S0002-9947-04-03647-5&rft_dat=%3Cjstor_pasca%3E3844962%3C/jstor_pasca%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=3844962&rfr_iscdi=true |