dorsal/arxiv
View SchemaNoninvertibility and ``Semi-'' Analogs of (Super) Manifolds, Fiber Bundles and Homotopies
| Authors | Steven Duplij |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9609022 |
| URL | https://arxiv.org/abs/q-alg/9609022 |
Abstract
Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to redefine such fundamental notions as supermanifolds, fiber bundles and homotopies using some weakening invertibility conditions. The prefix semi- reflects the fact that the underlying morphisms form corresponding semigroups consisting of a known group part and a new ideal noninvertible part. We found that the absence of invertibility gives us the generalization of the cocycle conditions for transition functions of supermanifolds and fiber bundles in a natural way, which can lead to construction of noninvertible analogs of \v{C}ech cocycles. We define semi-homotopies, which can be noninvertible and describe mappings into the semi-supermanifolds introduced.
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"abstract": "Supersymmetry contains initially noninvertible objects, but it is common to\ndeal with the invertible ones only, factorizing former in some extent. We\npropose to reconsider this ansatz and try to redefine such fundamental notions\nas supermanifolds, fiber bundles and homotopies using some weakening\ninvertibility conditions. The prefix semi- reflects the fact that the\nunderlying morphisms form corresponding semigroups consisting of a known group\npart and a new ideal noninvertible part. We found that the absence of\ninvertibility gives us the generalization of the cocycle conditions for\ntransition functions of supermanifolds and fiber bundles in a natural way,\nwhich can lead to construction of noninvertible analogs of \\v{C}ech cocycles.\nWe define semi-homotopies, which can be noninvertible and describe mappings\ninto the semi-supermanifolds introduced.",
"arxiv_id": "q-alg/9609022",
"authors": [
"Steven Duplij"
],
"categories": [
"q-alg",
"alg-geom",
"dg-ga",
"funct-an",
"hep-th",
"math.AG",
"math.DG",
"math.FA",
"math.QA"
],
"title": "Noninvertibility and ``Semi-\u0027\u0027 Analogs of (Super) Manifolds, Fiber Bundles and Homotopies",
"url": "https://arxiv.org/abs/q-alg/9609022"
},
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