Work

The equalities of interleaving distances and cohomology interleavings of spaces over $$BS^1$$

Year: 2026

Type: article

Abstract: The cohomology interleaving distance (CohID) is defined and considered in the category of persistent differential graded modules over a field. As a consequence, we show that, in the category, the distance coincides with the homotopy commutative interleaving distance , the homotopy interleaving distance originally due to Blumberg and Lesnick, and the interleaving distance in the homotopy category in the sense of Lanari and Scoccola. Moreover, we apply the CohID to spaces over the classifying space $$BS^1$$ B S 1 of the circle group via the singular cochain functor. Then, upper and lower bounds of the CohID are investigated with the cup-lengths of spaces over $$BS^1$$ B S 1 . As a computational example, we explicitly determine the CohID for complex projective spaces by utilizing the bottleneck distance of barcodes associated with the cohomology of the spaces.

Source: Journal of Applied and Computational Topology

DOI: 10.1007/s41468-026-00252-0

Authors: Katsuhiko Kuribayashi, Takahito Naito, Shun Wakatsuki, Toshihiro Yamaguchi

Institutions: Shinshu University, Nippon Institute of Technology, Nagoya University, University of Kochi, Kōchi University

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funder: Japan Society for the Promotion of Science