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Mapping Graph Homology to -Theory of Roe Algebras
Given a graph , one may consider the set of its vertices as a metric space by assuming that all edges have length one. We consider two versions of homology theory of and their -theory counterparts — the -theory of the (uniform) Roe algebra of the metric space of vertices of . We construct here a nat...
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| Published in: | Russian journal of mathematical physics 2024, Vol.31 (1), p.132-136 |
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| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-p1402-318c5a1005b0bef7dee0b28ab390530aa1ec02f01dbcfbf092dd5d208cdc89cb3 |
| container_end_page | 136 |
| container_issue | 1 |
| container_start_page | 132 |
| container_title | Russian journal of mathematical physics |
| container_volume | 31 |
| creator | Manuilov, V. |
| description | Given a graph
, one may consider the set
of its vertices as a metric space by assuming that all edges have length one. We consider two versions of homology theory of
and their
-theory counterparts — the
-theory of the (uniform) Roe algebra of the metric space
of vertices of
. We construct here a natural mapping from homology of
to the
-theory of the Roe algebra of
, and its uniform version. We show that, when
is the Cayley graph of
, the constructed mappings are isomorphisms.
DOI
10.1134/S106192084010102 |
| doi_str_mv | 10.1134/S106192084010102 |
| format | article |
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, one may consider the set
of its vertices as a metric space by assuming that all edges have length one. We consider two versions of homology theory of
and their
-theory counterparts — the
-theory of the (uniform) Roe algebra of the metric space
of vertices of
. We construct here a natural mapping from homology of
to the
-theory of the Roe algebra of
, and its uniform version. We show that, when
is the Cayley graph of
, the constructed mappings are isomorphisms.
DOI
10.1134/S106192084010102</description><identifier>ISSN: 1061-9208</identifier><identifier>EISSN: 1555-6638</identifier><identifier>DOI: 10.1134/S106192084010102</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>14/34 ; 639/766/189 ; 639/766/530 ; 639/766/747 ; Algebra ; Apexes ; Graph theory ; Homology ; Isomorphism ; Mapping ; Mathematical and Computational Physics ; Metric space ; Physics ; Physics and Astronomy ; Theoretical</subject><ispartof>Russian journal of mathematical physics, 2024, Vol.31 (1), p.132-136</ispartof><rights>Pleiades Publishing, Ltd. 2024</rights><rights>Pleiades Publishing, Ltd. 2024.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p1402-318c5a1005b0bef7dee0b28ab390530aa1ec02f01dbcfbf092dd5d208cdc89cb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Manuilov, V.</creatorcontrib><title>Mapping Graph Homology to -Theory of Roe Algebras</title><title>Russian journal of mathematical physics</title><addtitle>Russ. J. Math. Phys</addtitle><description>Given a graph
, one may consider the set
of its vertices as a metric space by assuming that all edges have length one. We consider two versions of homology theory of
and their
-theory counterparts — the
-theory of the (uniform) Roe algebra of the metric space
of vertices of
. We construct here a natural mapping from homology of
to the
-theory of the Roe algebra of
, and its uniform version. We show that, when
is the Cayley graph of
, the constructed mappings are isomorphisms.
DOI
10.1134/S106192084010102</description><subject>14/34</subject><subject>639/766/189</subject><subject>639/766/530</subject><subject>639/766/747</subject><subject>Algebra</subject><subject>Apexes</subject><subject>Graph theory</subject><subject>Homology</subject><subject>Isomorphism</subject><subject>Mapping</subject><subject>Mathematical and Computational Physics</subject><subject>Metric space</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Theoretical</subject><issn>1061-9208</issn><issn>1555-6638</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpdkEFLAzEQhYMoWKt3jwHP0Zlks02OpWgrVASt5yXJZreWtYlJe-i_N6WCIHOYgfcx8-YRcotwjyiqh3eEGjUHVQGW4mdkhFJKVtdCnZe5qOwoX5KrnDcANSioRgRfTIyf257Ok4lrughfYQj9ge4CZau1D-lAQ0ffgqfTofc2mXxNLjozZH_z28fk4-lxNVuw5ev8eTZdsogVcCZQOWkQQFqwvpu03oPlylihQQowBr0D3gG21nW2A83bVrbFoGud0s6KMbk77Y0pfO993jWbsE_bcrLhulYaq2pSFwpPVI6pvOHTH4XQHJNp_icjfgAiVFRG</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Manuilov, V.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2024</creationdate><title>Mapping Graph Homology to -Theory of Roe Algebras</title><author>Manuilov, V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p1402-318c5a1005b0bef7dee0b28ab390530aa1ec02f01dbcfbf092dd5d208cdc89cb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>14/34</topic><topic>639/766/189</topic><topic>639/766/530</topic><topic>639/766/747</topic><topic>Algebra</topic><topic>Apexes</topic><topic>Graph theory</topic><topic>Homology</topic><topic>Isomorphism</topic><topic>Mapping</topic><topic>Mathematical and Computational Physics</topic><topic>Metric space</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Manuilov, V.</creatorcontrib><jtitle>Russian journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Manuilov, V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Mapping Graph Homology to -Theory of Roe Algebras</atitle><jtitle>Russian journal of mathematical physics</jtitle><stitle>Russ. J. Math. Phys</stitle><date>2024</date><risdate>2024</risdate><volume>31</volume><issue>1</issue><spage>132</spage><epage>136</epage><pages>132-136</pages><issn>1061-9208</issn><eissn>1555-6638</eissn><abstract>Given a graph
, one may consider the set
of its vertices as a metric space by assuming that all edges have length one. We consider two versions of homology theory of
and their
-theory counterparts — the
-theory of the (uniform) Roe algebra of the metric space
of vertices of
. We construct here a natural mapping from homology of
to the
-theory of the Roe algebra of
, and its uniform version. We show that, when
is the Cayley graph of
, the constructed mappings are isomorphisms.
DOI
10.1134/S106192084010102</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S106192084010102</doi><tpages>5</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1061-9208 |
| ispartof | Russian journal of mathematical physics, 2024, Vol.31 (1), p.132-136 |
| issn | 1061-9208 1555-6638 |
| language | eng |
| recordid | cdi_proquest_journals_2968914476 |
| source | Springer Link |
| subjects | 14/34 639/766/189 639/766/530 639/766/747 Algebra Apexes Graph theory Homology Isomorphism Mapping Mathematical and Computational Physics Metric space Physics Physics and Astronomy Theoretical |
| title | Mapping Graph Homology to -Theory of Roe Algebras |
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