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[Texts]## 57M: Low-dimensional topology |

- 57M05: Fundamental group, presentations, free differential calculus
- 57M07: Topological methods in group theory
- 57M10: Covering spaces
- 57M12: Special coverings, e.g. branched
- 57M15: Relations with graph theory, See also 05Cxx
- 57M20: Two-dimensional complexes
- 57M25: Knots and links in S^3, For higher dimensions, See 57Q45
- 57M27: Invariants of knots and 3-manifolds [new in 2000]
- 57M30: Wild knots and surfaces, etc., wild embeddings
- 57M35: Dehn's lemma, sphere theorem, loop theorem, asphericity
- 57M40: Characterizations of E^3 and S^3 (Poincaré conjecture), See also 57N12
- 57M50: Geometric structures on low-dimensional manifolds
- 57M60: Group actions in low dimensions
- 57M99: None of the above but in this section

Parent field: 57: Manifolds and Cell Complexes

Browse all (old) classifications for this area at the AMS.

A good survey paper is Raymond Lickorish, "Polynomials for Links", Bull. London Math. Soc. 20 (1988) 558-588. See also L. H. Kauffman's book "Knots and Physics".

Online Primer on Knot theory [Charilaos Aneziris]

Knot Plot, a program to visualize and manipulate knots in three and four dimensions

- Knot Square
- Atlas of oriented knots and links
- A physicist's view of Knots and Braids

- What is knot theory
- Do knot complements determine knot type?
- Distinct links with homeomorphic complements in S^3
- Whitney's Theorem classifying immersions of circles into the plane
- Papakyriakopolous' Theorems (historical)
- Parameterizing a tubular neighborhood of a knot.
- Alexander's horned sphere and other wild embeddings of S^2 into S^3
- References to computational knot theory
- The computational complexity of knot and link problems
- How hard is it to distinguish among knots?
- Can one determine whether a knot is really knotted from its projection to the plane?
- Triangulating polygons in R^3 -- when is it even possible? (problems if knotted)
- Curves in R^4 are unknotted; generalize?
- The Smith conjecture: fixed points under periodic homeomorphisms of the sphere are unknotted.
- Connections between knot theory and statistical mechanics (the Jones polynomial)
- Literature highlights: Knot theory and Functional Analysis
- Applications of the Schönflies theorem
- The p-colorability of knots and the dihedral groups
- Conway's game of rational tangles (a two-strand braid).

Last modified 2001/10/14 by Dave Rusin. Mail: