Surgery and bordism groups in quantum partial differential equations. I: The quantum Poincaré conjecture
In this work, in two parts, we continue to develop the geometric theory of quantum PDE’s, introduced by us starting from 1996. (The second part is quoted in Prástaro [A. Prástaro, Surgery and bordism groups in quantum partial differential equations. II: Variational quantum PDE’s, Nonlinear Anal. TMA...
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description | In this work, in two parts, we continue to develop the geometric theory of quantum PDE’s, introduced by us starting from 1996. (The second part is quoted in Prástaro [A. Prástaro, Surgery and bordism groups in quantum partial differential equations. II: Variational quantum PDE’s, Nonlinear Anal. TMA, in press (
10.1016/j.na.2008.10.063)]) This theory has the purpose to build a rigorous mathematical theory of PDE’s in the category
D
S
of noncommutative manifolds (
quantum (super)manifolds), necessary to encode physical phenomena at microscopic level (i.e.,
quantum level). Aim of the present paper is to report on some new issues in this direction, emphasizing an interplaying between surgery, integral bordism groups and conservations laws. In particular, a proof of the Poincaré conjecture, generalized to the category
D
S
, is given by using our geometric theory of PDE’s just in such a category. |
doi_str_mv | 10.1016/j.na.2008.11.077 |
format | Article |
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10.1016/j.na.2008.10.063)]) This theory has the purpose to build a rigorous mathematical theory of PDE’s in the category
D
S
of noncommutative manifolds (
quantum (super)manifolds), necessary to encode physical phenomena at microscopic level (i.e.,
quantum level). Aim of the present paper is to report on some new issues in this direction, emphasizing an interplaying between surgery, integral bordism groups and conservations laws. In particular, a proof of the Poincaré conjecture, generalized to the category
D
S
, is given by using our geometric theory of PDE’s just in such a category.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2008.11.077</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Categories ; Conservation laws ; Construction ; Existence of local and global solutions in noncommutative PDE’s ; Integral bordisms in PDE’s ; Mathematical analysis ; Nonlinearity ; Partial differential equations ; Poincaré conjecture ; Presses ; Surgery</subject><ispartof>Nonlinear analysis, 2009-12, Vol.71 (12), p.e502-e525</ispartof><rights>2008 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c326t-38a7af3e556ffbc68e172d91b6fdf7c128edd457c7e512cb6bee58b787a945493</citedby><cites>FETCH-LOGICAL-c326t-38a7af3e556ffbc68e172d91b6fdf7c128edd457c7e512cb6bee58b787a945493</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0362546X08006986$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Prastaro, Agostino</creatorcontrib><title>Surgery and bordism groups in quantum partial differential equations. I: The quantum Poincaré conjecture</title><title>Nonlinear analysis</title><description>In this work, in two parts, we continue to develop the geometric theory of quantum PDE’s, introduced by us starting from 1996. (The second part is quoted in Prástaro [A. Prástaro, Surgery and bordism groups in quantum partial differential equations. II: Variational quantum PDE’s, Nonlinear Anal. TMA, in press (
10.1016/j.na.2008.10.063)]) This theory has the purpose to build a rigorous mathematical theory of PDE’s in the category
D
S
of noncommutative manifolds (
quantum (super)manifolds), necessary to encode physical phenomena at microscopic level (i.e.,
quantum level). Aim of the present paper is to report on some new issues in this direction, emphasizing an interplaying between surgery, integral bordism groups and conservations laws. In particular, a proof of the Poincaré conjecture, generalized to the category
D
S
, is given by using our geometric theory of PDE’s just in such a category.</description><subject>Categories</subject><subject>Conservation laws</subject><subject>Construction</subject><subject>Existence of local and global solutions in noncommutative PDE’s</subject><subject>Integral bordisms in PDE’s</subject><subject>Mathematical analysis</subject><subject>Nonlinearity</subject><subject>Partial differential equations</subject><subject>Poincaré conjecture</subject><subject>Presses</subject><subject>Surgery</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp1kM1KAzEURoMoWKt7l9m5mjGZNMm0OxF_CgUFK7gLmeSmprRJm8wIfSSfwxdzasWdq8vlnu_CdxC6pKSkhIrrZRl0WRFSl5SWRMojNKC1ZAWvKD9GA8JEVfCReDtFZzkvCSFUMjFA_qVLC0g7rIPFTUzW5zVepNhtMvYBbzsd2m6NNzq1Xq-w9c5BgvCzQH9tfQy5xNMJnr_DH_4cfTA6fX1iE8MSTNslOEcnTq8yXPzOIXq9v5vfPhazp4fp7c2sMKwSbcFqLbVjwLlwrjGiBiorO6aNcNZJQ6sarB1xaSRwWplGNAC8bmQt9XjER2M2RFeHv5sUtx3kVq19NrBa6QCxy2rc2xKMMtaT5ECaFHNO4NQm-bVOO0WJ2ktVSxW02ktVlKpeah-ZHCLQN_jwkFQ2HoIB61NfU9no_w9_A4vsgY8</recordid><startdate>20091215</startdate><enddate>20091215</enddate><creator>Prastaro, Agostino</creator><general>Elsevier Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20091215</creationdate><title>Surgery and bordism groups in quantum partial differential equations. I: The quantum Poincaré conjecture</title><author>Prastaro, Agostino</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c326t-38a7af3e556ffbc68e172d91b6fdf7c128edd457c7e512cb6bee58b787a945493</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Categories</topic><topic>Conservation laws</topic><topic>Construction</topic><topic>Existence of local and global solutions in noncommutative PDE’s</topic><topic>Integral bordisms in PDE’s</topic><topic>Mathematical analysis</topic><topic>Nonlinearity</topic><topic>Partial differential equations</topic><topic>Poincaré conjecture</topic><topic>Presses</topic><topic>Surgery</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Prastaro, Agostino</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Prastaro, Agostino</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Surgery and bordism groups in quantum partial differential equations. I: The quantum Poincaré conjecture</atitle><jtitle>Nonlinear analysis</jtitle><date>2009-12-15</date><risdate>2009</risdate><volume>71</volume><issue>12</issue><spage>e502</spage><epage>e525</epage><pages>e502-e525</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><abstract>In this work, in two parts, we continue to develop the geometric theory of quantum PDE’s, introduced by us starting from 1996. (The second part is quoted in Prástaro [A. Prástaro, Surgery and bordism groups in quantum partial differential equations. II: Variational quantum PDE’s, Nonlinear Anal. TMA, in press (
10.1016/j.na.2008.10.063)]) This theory has the purpose to build a rigorous mathematical theory of PDE’s in the category
D
S
of noncommutative manifolds (
quantum (super)manifolds), necessary to encode physical phenomena at microscopic level (i.e.,
quantum level). Aim of the present paper is to report on some new issues in this direction, emphasizing an interplaying between surgery, integral bordism groups and conservations laws. In particular, a proof of the Poincaré conjecture, generalized to the category
D
S
, is given by using our geometric theory of PDE’s just in such a category.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2008.11.077</doi></addata></record> |
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subjects | Categories Conservation laws Construction Existence of local and global solutions in noncommutative PDE’s Integral bordisms in PDE’s Mathematical analysis Nonlinearity Partial differential equations Poincaré conjecture Presses Surgery |
title | Surgery and bordism groups in quantum partial differential equations. I: The quantum Poincaré conjecture |
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