This course introduces students to combinatorial methods in low-dimensional topology, using knot theory and periodic tangles as the main guiding examples. The course begins with classical knots, links, diagrams, Reidemeister moves, polynomial invariants, braids, and Seifert surfaces, and then broadens toward surfaces, 3-manifolds, skein modules, and algebraic structures arising from diagrammatic topology.
The main theme is the translation of topological questions into combinatorial and algebraic language. Students will see how diagrams encode topology, how local moves describe equivalence, how skein relations produce invariants, and how braid-theoretic methods connect topology with algebra. The final part of the course focuses on generalized and periodic settings, especially doubly periodic tangles, where motifs, lattices, and periodic equivalence lead to current research questions.
The course emphasizes diagrams, examples, rigorous definitions, and structural thinking, and is intended as a bridge from classical knot theory to modern research directions in low-dimensional and periodic topology.
- Docent: Ioannis Diamantis