I have never studied knot theory before. I would like to get into the subject. I am interested in studying knots from a topological perspective (as opposed to a combinatorial one.) I am studying knot theory to eventually be able to read Morishita's Knots and Primes.
I would like to begin my studies by reading Neuwirth's Knot Groups. I have questions:
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For someone with little prior knowledge in knot theory, am I starting too big? Would reading Neuwirth be a fruitless endeavor? What articles or texts should I look into before reading Neuwirth, if any?
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Knot Groups was published in 1965. There has been much work in the area since then. Is there a newer superior to Neuwirth? Toward my goal of reading Morishita, what knot theory-related texts should I consider as substitutes and/or supplements to Neuwirth, if any? (The reason I want to start with Neuwirth is because I know knot groups are of fundamental importance to Morishita's work, so it seemed natural to start learning knot groups.)
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What are the most important prerequisites to Knot Groups? I understand this is broad. I don't need specifics, but broadly identifying the most important tools I will need going into Neuwirth would be very helpful. (This is similar to my first question.)
Best Answer
I would say the only prerequisites are a bit of abstract algebra applied to cellular decompositions of 3-manifolds. Chapter III of the book is a reasonably self-contained explanation of the classical origins of knot theory -- with many illustrations fully described in words, but left to the imagination of the reader as pictures. The is book is greatly underappreciated, perhaps because of its misleading title. It's really more about covering complexes than the knot group itself. --Ken Perko, [email protected]