Author Topic: Knot Theory  (Read 4514 times)

Mike in MD

  • Full Member
  • ***
  • Posts: 40
Knot Theory
« on: January 06, 2012, 03:31:18 PM »
Anybody interested in working through

Knots, Links, Braids and 3-Manifolds
by V.V. Prasolov and A.B. Sossinsky
(subtitle: An Introduction to the New Invariants in Low-Dimensional Topology)

You can see it on Amazon at

http://www.amazon.com/Knots-Links-Braids-3-Manifolds-Low-Dimensional/dp/0821808982/ref=sr_1_5?s=books&ie=UTF8&qid=1325857644&sr=1-5

The price is a little steep, but that's what you get with math books.

Look over the first few pages.  This has been on my to-do list for a few years, but other things keep coming up.  Right now, it's representation theory of Lie groups. 

This is clearly a math book that uses knots as a tool, rather than a knot book like ABOK.  You probably should have group theory and topology before trying it.  I decided to post this because Xarax has started a thread about knot invariants like winding numbers. 

The authors put solutions of some of the problems in the back, in support of their claim to be elementary.

Anyway, don't everyone respond at the same time.  You will overwhelm the forum server.   :)

Mike

Mike in MD

  • Full Member
  • ***
  • Posts: 40
Re: Knot Theory
« Reply #1 on: January 10, 2012, 04:47:33 PM »
I just realized that the Jones polynomial which is the subject of this book is the creation of none other than Prof Vaughan Jones FRS, who is a Vice President of the IGKT.  I am a combination of embarrassed and impressed with the IGKT.

Mike


KnotMe

  • Sr. Member
  • *****
  • Posts: 570
    • The Dao of Silk
Re: Knot Theory
« Reply #2 on: January 11, 2012, 09:43:53 AM »
Pretty sure you're on your own, boyo.  8)

Colin Adam's The Knot Book has been on my todo list for almost 2 decades and I've never gotten around to it and KLB3 there is orders of magnitude past that.

Mike in MD

  • Full Member
  • ***
  • Posts: 40
Re: Knot Theory
« Reply #3 on: January 11, 2012, 07:49:15 PM »
Hi Carol,

The Colin Adams book looks interesting.  It gets to the Jones polynomial.  If you decide to end your two decade wait and want to do a *group study*, let me know and I will get a copy.  Maybe you could convince a third to join.

Mike

KnotMe

  • Sr. Member
  • *****
  • Posts: 570
    • The Dao of Silk
Re: Knot Theory
« Reply #4 on: January 11, 2012, 08:08:06 PM »
Yes, on intent.  No promises WRT timing... 8)

struktor

  • Sr. Member
  • *****
  • Posts: 279
Re: Knot Theory
« Reply #5 on: September 14, 2014, 09:28:18 AM »
Look at Knot Theory
http://arxiv.org/abs/1105.2238v1

Free download :)