3 papers
math.ST2026
The Topological Stability Index: A Variance-Based Measure for Persistence Barcodes
Joris Kirchner, Ioannis Diamantis
We introduce the \emph{Topological Stability Index} (TSI), a variance-based scalar measure for persistence barcodes that quantifies the dispersion of persistence lifetimes. Unlike…
math.GT2026
Stuck Knots: Rigidity, Invariants, and Unsticking Distance
Ioannis Diamantis
A {\it stuck knot} is a knot diagram containing designated crossings, called {\it stuck crossings}, whose incident strands are required to remain locally non-separable. These rigid…
math.HO2025
The VIBE Framework: A Student-Centered Approach to Teaching Knot Theory in Secondary Mathematics
Ioannis Diamantis
Knot theory, a visual and intuitive branch of topology, offers a unique opportunity to introduce advanced mathematical thinking in secondary education. Despite its accessibility an…