A geometrisation of $\mathbb N$-manifolds
This paper proposes a geometrisation of $\mathbb N$-manifolds of degree $n$ as $n$-fold vector bundles equipped with a (signed) $S_n$-symmetry. More precisely, it proves an equivalence between the categories of $[n]$-manifolds and the category of symmetric $n$-fold vector bundles, by finding that sy...
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| creator | Heuer, Malte Jotz, Madeleine |
| description | This paper proposes a geometrisation of $\mathbb N$-manifolds of degree $n$
as $n$-fold vector bundles equipped with a (signed) $S_n$-symmetry.
More precisely, it proves an equivalence between the categories of
$[n]$-manifolds and the category of symmetric $n$-fold vector bundles, by
finding that symmetric $n$-fold vector bundle cocycles and $[n]$-manifold
cocycles are identical.
This extends the already known equivalences of $[1]$-manifolds with vector
bundles, and of $[2]$-manifolds with involutive double vector bundles, where
the involution is understood as an $S_2$-action. |
| doi_str_mv | 10.48550/arxiv.2305.19851 |
| format | Article |
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as $n$-fold vector bundles equipped with a (signed) $S_n$-symmetry.
More precisely, it proves an equivalence between the categories of
$[n]$-manifolds and the category of symmetric $n$-fold vector bundles, by
finding that symmetric $n$-fold vector bundle cocycles and $[n]$-manifold
cocycles are identical.
This extends the already known equivalences of $[1]$-manifolds with vector
bundles, and of $[2]$-manifolds with involutive double vector bundles, where
the involution is understood as an $S_2$-action.</description><identifier>DOI: 10.48550/arxiv.2305.19851</identifier><language>eng</language><subject>Mathematics - Differential Geometry ; Mathematics - Mathematical Physics ; Physics - Mathematical Physics</subject><creationdate>2023-05</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2305.19851$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2305.19851$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Heuer, Malte</creatorcontrib><creatorcontrib>Jotz, Madeleine</creatorcontrib><title>A geometrisation of $\mathbb N$-manifolds</title><description>This paper proposes a geometrisation of $\mathbb N$-manifolds of degree $n$
as $n$-fold vector bundles equipped with a (signed) $S_n$-symmetry.
More precisely, it proves an equivalence between the categories of
$[n]$-manifolds and the category of symmetric $n$-fold vector bundles, by
finding that symmetric $n$-fold vector bundle cocycles and $[n]$-manifold
cocycles are identical.
This extends the already known equivalences of $[1]$-manifolds with vector
bundles, and of $[2]$-manifolds with involutive double vector bundles, where
the involution is understood as an $S_2$-action.</description><subject>Mathematics - Differential Geometry</subject><subject>Mathematics - Mathematical Physics</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzr0OgjAUhuEuDga9ACcZXBzAtqeFMhLiX0J00NGEHKDVJgIGiNG79_db3u3LQ8iEUV8oKekC24e9-xyo9FmkJBuSeeyedVPpvrUd9rap3ca4s1OF_SXP3d3Mq7C2prmW3YgMDF47Pf7XIYfV8phsvHS_3iZx6mEQMq8EEYSAEGmtGUYBB5azPJACuOIFp8pwpgVFAe9RiYIbo4QoNMgwBAUOmf5ev9Ts1toK22f2IWdfMrwAKXk46g</recordid><startdate>20230531</startdate><enddate>20230531</enddate><creator>Heuer, Malte</creator><creator>Jotz, Madeleine</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230531</creationdate><title>A geometrisation of $\mathbb N$-manifolds</title><author>Heuer, Malte ; Jotz, Madeleine</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-d34673a39eee1a96231b1b6543282c208f21e40a4333305a42ff844ce3577383</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Differential Geometry</topic><topic>Mathematics - Mathematical Physics</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Heuer, Malte</creatorcontrib><creatorcontrib>Jotz, Madeleine</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Heuer, Malte</au><au>Jotz, Madeleine</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A geometrisation of $\mathbb N$-manifolds</atitle><date>2023-05-31</date><risdate>2023</risdate><abstract>This paper proposes a geometrisation of $\mathbb N$-manifolds of degree $n$
as $n$-fold vector bundles equipped with a (signed) $S_n$-symmetry.
More precisely, it proves an equivalence between the categories of
$[n]$-manifolds and the category of symmetric $n$-fold vector bundles, by
finding that symmetric $n$-fold vector bundle cocycles and $[n]$-manifold
cocycles are identical.
This extends the already known equivalences of $[1]$-manifolds with vector
bundles, and of $[2]$-manifolds with involutive double vector bundles, where
the involution is understood as an $S_2$-action.</abstract><doi>10.48550/arxiv.2305.19851</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Differential Geometry Mathematics - Mathematical Physics Physics - Mathematical Physics |
| title | A geometrisation of $\mathbb N$-manifolds |
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