On Perrot's index cocycles Article Swipe
Jonathan Block
,
Nigel Higson
,
Jesús María Silva Sánchez
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2207.13411
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2207.13411
We shall present a simplified version of a construction due to Denis Perrot that recovers the Todd class of the complexified tangent bundle from a JLO-type cyclic cocycle. The construction takes place within an algebraic framework, rather than the customary functional-analytic framework for the JLO theory. The series expansion for the exponential function is used in place of the heat kernel from the functional-analytic theory; the Dirac operator chosen is far from elliptic; and a remarkable new trace discovered by Perrot replaces the operator trace. In its full form Perrot's theory constitutes a wholly new approach to index theory. The account presented here covers most but not all of this approach.
Related Topics
Concepts
TRACE (psycholinguistics)
Tangent
Pure mathematics
Operator (biology)
Function (biology)
Algebraic number
Analytic function
Bundle
Algebra over a field
Mathematics
Mathematical analysis
Philosophy
Geometry
Gene
Transcription factor
Repressor
Materials science
Evolutionary biology
Biology
Chemistry
Biochemistry
Linguistics
Composite material
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2207.13411
- https://arxiv.org/pdf/2207.13411
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4288727292
All OpenAlex metadata
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https://openalex.org/W4288727292Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2207.13411Digital Object Identifier
- Title
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On Perrot's index cocyclesWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-07-27Full publication date if available
- Authors
-
Jonathan Block, Nigel Higson, Jesús María Silva SánchezList of authors in order
- Landing page
-
https://arxiv.org/abs/2207.13411Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2207.13411Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2207.13411Direct OA link when available
- Concepts
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TRACE (psycholinguistics), Tangent, Pure mathematics, Operator (biology), Function (biology), Algebraic number, Analytic function, Bundle, Algebra over a field, Mathematics, Mathematical analysis, Philosophy, Geometry, Gene, Transcription factor, Repressor, Materials science, Evolutionary biology, Biology, Chemistry, Biochemistry, Linguistics, Composite materialTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.complexified | 20 |
| abstract_inverted_index.construction | 8, 29 |
| abstract_inverted_index.functional-analytic | 40, 63 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/11 |
| sustainable_development_goals[0].score | 0.5400000214576721 |
| sustainable_development_goals[0].display_name | Sustainable cities and communities |
| citation_normalized_percentile |