Treffer: Exploring Connections Between Topological Invariants and Computational Complexity: A Modest Investigation
Title:
Exploring Connections Between Topological Invariants and Computational Complexity: A Modest Investigation
Publisher Information:
Zenodo
Publication Year:
2025
Collection:
Zenodo
Subject Terms:
Document Type:
Fachzeitschrift
text
Language:
English
Relation:
https://zenodo.org/records/17217609; oai:zenodo.org:17217609; https://doi.org/10.5281/zenodo.17217609
DOI:
10.5281/zenodo.17217609
Rights:
Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode ; Paulo Sérgio de Andrade
Accession Number:
edsbas.55C5CE
Database:
BASE
Weitere Informationen
We investigate potential relationships between certain topological invariants of 3-dimensional manifolds and the computational complexity of related algorithmic problems. Specifically, we examine whether properties of fundamental groups correlate with the difficulty of knot recognition algorithms. Through computational experiments on a database of prime knots with up to 10 crossings, we identify preliminary patterns that suggest deeper connections worth further investigation. Our results are modest but concrete, providing a foundation for more systematic study of topology-computation relationships. Classification: Primary 57M25, 68Q17; Secondary 55N10, 68Q15