English

Rational relative sectional category

Algebraic Topology 2026-04-28 v1

Abstract

We develop an algebraic model for the relative sectional category of a continuous map in rational homotopy theory using commutative differential graded algebras (CDGAs). Our main result establishes that for formal maps, the rational relative sectional category can be computed purely from cohomology, using ideal nilpotency. We also show that this equality may fail in general topological settings. Applying this framework, we obtain purely algebraic characterizations for the rational Lusternik-Schnirelmann category and the rational higher topological complexity of a map. Finally, we provide an algebraic description of the rational homotopic distance between formal maps.

Keywords

Cite

@article{arxiv.2604.23395,
  title  = {Rational relative sectional category},
  author = {Lekha Das and Bittu Singh},
  journal= {arXiv preprint arXiv:2604.23395},
  year   = {2026}
}

Comments

22 pages. comments are welcome

R2 v1 2026-07-01T12:35:16.643Z