On the $m$-dimensional sectional category and induced invariants
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909985453113344 |
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| author | Arora, Ramandeep Singh Datta, Sutirtha Daundkar, Navnath Dutta, Gopal Chandra |
| author_facet | Arora, Ramandeep Singh Datta, Sutirtha Daundkar, Navnath Dutta, Gopal Chandra |
| contents | In this paper, we systematically study the $m$-dimensional sectional category of a fibration, introduced by Schwarz, as an approximating invariant for the sectional category. We develop the basic theory of this invariant, establish its fundamental properties, and show how it gives rise to a hierarchy of induced invariants, including the $m$-dimensional Lusternik-Schnirelmann category, the $m$-topological complexity, and the $m$-homotopic distance between maps. We further investigate the relationships between these $m$-dimensional invariants and their classical analogues, present a variety of examples in which these invariants are computed, and illustrate when they agree with or differ from their classical counterparts. We also introduce the notion of $m$-cohomological distance and study its interaction with the $m$-homotopic distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05334 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the $m$-dimensional sectional category and induced invariants Arora, Ramandeep Singh Datta, Sutirtha Daundkar, Navnath Dutta, Gopal Chandra Algebraic Topology 55M30, 55P45, 55R10 In this paper, we systematically study the $m$-dimensional sectional category of a fibration, introduced by Schwarz, as an approximating invariant for the sectional category. We develop the basic theory of this invariant, establish its fundamental properties, and show how it gives rise to a hierarchy of induced invariants, including the $m$-dimensional Lusternik-Schnirelmann category, the $m$-topological complexity, and the $m$-homotopic distance between maps. We further investigate the relationships between these $m$-dimensional invariants and their classical analogues, present a variety of examples in which these invariants are computed, and illustrate when they agree with or differ from their classical counterparts. We also introduce the notion of $m$-cohomological distance and study its interaction with the $m$-homotopic distance. |
| title | On the $m$-dimensional sectional category and induced invariants |
| topic | Algebraic Topology 55M30, 55P45, 55R10 |
| url | https://arxiv.org/abs/2601.05334 |