Pseudohomology and homology
The notion of a pseudocycle is introduced by McDuff and Salamon (J-holomorphic curves and quantum cohomology, University Lecture Series, Vol. 6, AMS (1994)) to provide a framework for defining Gromov-Witten invariants and quantum cohomology. This paper studies the bordism groups of pseudocycles, cal...
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| creator | Kahn, Peter J |
| description | The notion of a pseudocycle is introduced by McDuff and Salamon
(J-holomorphic curves and quantum cohomology, University Lecture Series, Vol.
6, AMS (1994)) to provide a framework for defining Gromov-Witten invariants and
quantum cohomology. This paper studies the bordism groups of pseudocycles,
called pseudohomology groups. These are shown to satisfy the Eilenberg-Steenrod
axioms. For smooth compact manifold pairs, it is proved that pseudohomology is
naturally equivalent to homology. Easy examples show that this equivalence does
not extend to the case of non-compact manifolds. |
| doi_str_mv | 10.48550/arxiv.math/0111223 |
| format | Article |
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(J-holomorphic curves and quantum cohomology, University Lecture Series, Vol.
6, AMS (1994)) to provide a framework for defining Gromov-Witten invariants and
quantum cohomology. This paper studies the bordism groups of pseudocycles,
called pseudohomology groups. These are shown to satisfy the Eilenberg-Steenrod
axioms. For smooth compact manifold pairs, it is proved that pseudohomology is
naturally equivalent to homology. Easy examples show that this equivalence does
not extend to the case of non-compact manifolds.</description><identifier>DOI: 10.48550/arxiv.math/0111223</identifier><language>eng</language><subject>Mathematics - Algebraic Topology ; Mathematics - Symplectic Geometry</subject><creationdate>2001-11</creationdate><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/math/0111223$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.math/0111223$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kahn, Peter J</creatorcontrib><title>Pseudohomology and homology</title><description>The notion of a pseudocycle is introduced by McDuff and Salamon
(J-holomorphic curves and quantum cohomology, University Lecture Series, Vol.
6, AMS (1994)) to provide a framework for defining Gromov-Witten invariants and
quantum cohomology. This paper studies the bordism groups of pseudocycles,
called pseudohomology groups. These are shown to satisfy the Eilenberg-Steenrod
axioms. For smooth compact manifold pairs, it is proved that pseudohomology is
naturally equivalent to homology. Easy examples show that this equivalence does
not extend to the case of non-compact manifolds.</description><subject>Mathematics - Algebraic Topology</subject><subject>Mathematics - Symplectic Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNo1zrsOgkAQheFtLIz6BDT4AOjOzi4DpTHeEhIt6MnILkoCYvASeXujYnXyNyefEB7ImY6MkXNuX-VzVvP9PJcAoBQOhXe4uYdtzk3dVM2p8_li_X-MxaDg6uYm_Y5Eul6ly22Q7De75SIJmACDCI20GANbI2O0CNpIyc6FqHXICpAsqYgpBIKCiSLCXOfuSFxobWOFIzH93X592bUta2677OPMeie-AYwcN9c</recordid><startdate>20011120</startdate><enddate>20011120</enddate><creator>Kahn, Peter J</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20011120</creationdate><title>Pseudohomology and homology</title><author>Kahn, Peter J</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a713-8350d391ad5093d314500aee63446a2137d728a76171fa77873c4ceb7af44d923</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Mathematics - Algebraic Topology</topic><topic>Mathematics - Symplectic Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Kahn, Peter J</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kahn, Peter J</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Pseudohomology and homology</atitle><date>2001-11-20</date><risdate>2001</risdate><abstract>The notion of a pseudocycle is introduced by McDuff and Salamon
(J-holomorphic curves and quantum cohomology, University Lecture Series, Vol.
6, AMS (1994)) to provide a framework for defining Gromov-Witten invariants and
quantum cohomology. This paper studies the bordism groups of pseudocycles,
called pseudohomology groups. These are shown to satisfy the Eilenberg-Steenrod
axioms. For smooth compact manifold pairs, it is proved that pseudohomology is
naturally equivalent to homology. Easy examples show that this equivalence does
not extend to the case of non-compact manifolds.</abstract><doi>10.48550/arxiv.math/0111223</doi><oa>free_for_read</oa></addata></record> |
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| identifier | DOI: 10.48550/arxiv.math/0111223 |
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| source | arXiv.org |
| subjects | Mathematics - Algebraic Topology Mathematics - Symplectic Geometry |
| title | Pseudohomology and homology |
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