4 ms·
What would people recommend to get up to speed on the alexander polynomial? The wikipedia page was terse as expected.
by QuadmasterXLII 1y ago
What would people recommend to get up to speed on the alexander polynomial? The wikipedia page was terse as expected.
- MarkusQ 1y agoFor a gentile introduction, Colin Adams's "The Knot Book" is very accessible (and builds up the notion of polynomial invariants step by step).
- bikenaga 1y agoYep, just noticed it's on my shelf - nice book! He describes Conway's approach to computing the Alexander polynomial using just two rules - a lot simpler than the technical stuff in Crowell and Fox.
- bikenaga 1y agoIt depends on your math background, but: Richard Crowell and Ralph Fox, "An Introduction to Knot Theory" (1963) - an old book which doesn't recent developments. The Dover edition is only $15.95: https://store.doverpublications.com/products/9780486468945?_pos=1&_ss=r https://store.doverpublications.com/products/9780486468945?_... Ralph Fox, "A Quick Trip Through Knot Theory" (1962). The original paper was a chapter in M. K. Fort's "Topology of 3-Manifolds" collection, but I think you can find copies online. Dale Rolfsen, "Knots and Links". A newer book and one of the best if you know some (algebraic) topology. He argue for considering the Alexander invariant (the homology of the infinite cyclic cover) rather than the Alexander polynomial. I don't have the newest edition, so I don't know how far it goes in terms of recent developments. The book by Burde and Zeischang has this stuff and more, but it's more advanced. I'm not a knot theorist, so I don't know about newer books - maybe someone else has better recommendations.