Feature Papers in Topology and Its Applications
A special issue of International Journal of Topology (ISSN 2813-9542).
Deadline for manuscript submissions: 31 December 2025 | Viewed by 1052
Special Issue Editor
Interests: topological quantum computing; epigenetics and epitranscriptomics; signal processing; geometry; quantum mechanics; discrete mathematics; graph theory; group theory; structural stability; communication; pure mathematics; topology
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
As the Editor-in-Chief of the International Journal of Topology, I am glad to propose the Special Issue “Feature Papers in Topology and Its Applications”, which is intended to be a collection of high-quality papers (original research articles or comprehensive reviews) addressing the subject of topology, either the general concepts and open conjectures or the applications to other fields of knowledge.
We welcome the submission of manuscripts from Editorial Board Members and outstanding scholars invited by the Editorial Board and the Editorial Office.
You are welcome to send short proposals for submissions of Feature Papers to our Editorial Office ([email protected]) for evaluation.
We expect that this inaugural issue will pave the way for the success of the new journal.
Dr. Michel Planat
Guest Editor
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. International Journal of Topology is an international peer-reviewed open access quarterly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- algebraic, geometric, and differential topology
- fuzzy topology
- manifolds, including low-dimensional ones, exotic manifolds
- topology and metric spaces
- homotopy, homology, cohomology
- measure theory
- theory of knots and links
- complexes
- openness, nearness, connectedness, continuity, compactness
- category theory, topoi
- topological combinatorics
- topological dynamics
- topological quantum computing
- applications of topology in biology, physics, computer science, robotics, engineering, etc.
Benefits of Publishing in a Special Issue
- Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
- Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
- Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
- External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
- e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.
Further information on MDPI's Special Issue polices can be found here.
Planned Papers
The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.
Title: About the Low Dimensional Topology Arising from the Modular Group
Authors: Michel Planat
Affiliation: CNRS, Institut FEMTO-ST, Université de Franche-Comté, F-25044 Besançon, France
Abstract: The modular group Γ = PSL(2, Z) and its congruence subgroups Γc play a central role in two-dimensional topology, being closely related to elliptic and modular curves, as well as modular forms. In
particular, every modular curve arises from the compactification of the extended upper-half plane via some congruence subgroup Γc. Notably, certain genus-zero modular curves are connected to the phenomenon of monstrous moonshine.
The modular lambda function λ(τ ), a Hauptmodul for the modular curve X(2) corresponding to the principal congruence subgroup Γ(2), also serves as the time parameter in the Painlev´e VI equation. These modular curves have significant applications in physics.
Since Γ is isomorphic to the fundamental group π1(T ) of the trefoil knot T = 31, d-fold covering spaces correspond to index-d subgroups of Γ. These subgroups are also related to the Kodaira classification of singular fibers for minimal elliptic surfaces. Potential applications to topological quantum computing are under active exploration.
In this paper, we review key aspects of the rich structure of Γ in the context of low-dimensional topology.
