A Hasse diagram for rational toral ranks
Toshihiro Yamaguchi

TL;DR
This paper introduces a Hasse diagram structure for classifying rational toral ranks of a simply connected CW complex, providing a new combinatorial perspective on almost free toral actions and their organization.
Contribution
It constructs a Hasse diagram for the poset of rationalized orbit spaces, linking algebraic invariants with topological structures in a novel way.
Findings
Defines a partial order on rationalized orbit spaces based on Borel fibrations.
Constructs a graph from the Hasse diagram and explores its properties.
Proposes viewing the graph as the skeleton of a CW complex.
Abstract
Let be a simply connected CW complex with finite rational cohomology. For the finite quotient set of rationalized orbit spaces of obtained by almost free toral actions, , induced by an equivalence relation based on rational toral ranks, we order as if there is a rationalized Borel fibration for some . It presents a variation of almost free toral actions on . We consider about the Hasse diagram of the poset , which makes a based graph , with some examples. Finally we will try to regard as the 1-skeleton of a finite CW complex with base point .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics
