Co-operational bivariant theory
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914816046661632 |
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| author | Yokura, Shoji |
| author_facet | Yokura, Shoji |
| contents | For a covariant functor W. Fulton and R. MacPherson defined \emph{an operational bivariant theory} associated to this covariant functor. In this paper we will show that given a contravariant functor one can similarly construct a ``dual" version of an operational bivariant theory, which we call a \emph{co-operational} bivariant theory. If a given contravariant functor is the usual cohomology theory, then our co-operational bivariant group for the identity map consists of what are usually called ``cohomology operations". In this sense, our co-operational bivariant theory consists of \emph{``generalized"} cohomology operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14516 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Co-operational bivariant theory Yokura, Shoji Algebraic Geometry Algebraic Topology For a covariant functor W. Fulton and R. MacPherson defined \emph{an operational bivariant theory} associated to this covariant functor. In this paper we will show that given a contravariant functor one can similarly construct a ``dual" version of an operational bivariant theory, which we call a \emph{co-operational} bivariant theory. If a given contravariant functor is the usual cohomology theory, then our co-operational bivariant group for the identity map consists of what are usually called ``cohomology operations". In this sense, our co-operational bivariant theory consists of \emph{``generalized"} cohomology operations. |
| title | Co-operational bivariant theory |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2306.14516 |