Knot Theory
Knot invariants, Jones and HOMFLY polynomials, and Khovanov homology.
Knot Theory. Knot invariants, Jones and HOMFLY polynomials, and Khovanov homology.
Foundations and canonical references
The standard treatments of knot theory approach the subject from complementary angles. Rolfsen, Knots and Links (2003) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Lickorish, An Introduction to Knot Theory (1997) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for knot theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2003Knots and Linksrolfsen-2003
- textbook · primary · 1997An Introduction to Knot Theorylickorish-1997
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