Exploring Connections Between Topological Invariants and Computational Complexity: A Modest Investigation
Year: 2025
Type: article
Abstract: 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
Author: SÉRGIO DE ANDRADE, PAULO
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083630145
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