{
  "annotation_id": "a67a2b12-1b33-452b-8d81-9e8629ab642d",
  "date_created": "2026-02-17T05:53:03.732000Z",
  "date_modified": "2026-02-17T05:53:03.732000Z",
  "file_hash": "8cfabc213d9fb32a00f53eaed8cff7aeb0679b3f865f2f8e0164501e1f04d1f4",
  "private": false,
  "record": {
    "abstract": "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.",
    "arxiv_id": "2601.05334",
    "authors": [
      "Ramandeep Singh Arora",
      "Sutirtha Datta",
      "Navnath Daundkar",
      "Gopal Chandra Dutta"
    ],
    "categories": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On the $m$-dimensional sectional category and induced invariants",
    "url": "https://arxiv.org/abs/2601.05334",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "acfd8428-f217-4580-b75e-c5de2e7229df",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}