Topology-book for self study about physical meaning

Question

I self study physics, and I have come across some mathematics that are unknown to me. It has to do with helicity, linking numbers and other topological factors.

A friend of mine told me that this is called topology. I want to delve into this subject on a mathematics basis but with some physical meaning in it. So I wanted to know if there are any books that are easy to delve into and can teach me these topological factors (especially stuff that have to do with linking numbers) but also give some intuition and maybe some physics exercises (or more generally have some exercises that are not purely mathematical).

Also, except from books,do you know any other means to learn these topological factors (like web sites)?

Thank you

this seems to be the book for you: http://www.amazon.com/Geometry-Topology-Physics-Edition-Graduate/dp/0750306068 — tired, May 18 '15 at 11:13
is there something for undergraduates?Because i am really interested in physics on undergraduate level(that has to do with undergraduate level mathematics) — TheQuantumMan, May 18 '15 at 11:17

score 1 · Accepted Answer · answered May 18 '15 at 11:20

1

I think Gauge Fields, Knots, and Gravity by Baez and Munian might be exactly what you're looking for. It is a very good text with plenty of illustrations that conveys good intuition about the mathematical and physical content. As per the title, the book discusses physical applications of knot theory, and the section starting on page 310 discusses linking numbers.

answered May 18 '15 at 11:20

ಠ_ಠ

10,682

is it a graduate studies book or undergraduate? It has some great reviews by the way – TheQuantumMan May 18 '15 at 11:31
I think it is accessible to both undergrads and grad students. It's definitely not a terse book. – ಠ_ಠ May 18 '15 at 12:39
1

just downloaded it,its great!thanx a lot! – TheQuantumMan May 18 '15 at 18:33

score -2 · Answer 2 · answered May 17 '15 at 23:18

-2

Metric spaces are basic to topological spaces. There is a book of only 71 pages where one can learn what is a ''distance'' with a high degree of intuition.

Yu. A. Shreider, WHAT IS DISTANCE, The Chicago university press, 1974. ISBN 0-226-75498-7.

answered May 17 '15 at 23:18

Idris Addou

4,193

so,it has to do with linking numbers and helicity? – TheQuantumMan May 17 '15 at 23:18
If you want to learn any matter which belongs to ''Topology'' you should at least learn what is a ''topology on a given set''. The resulting set is named ''topological space''. Among topological spaces there are some basic ones, they are too close to our intuition, they are ''metric spaces''. A metric space is a set endowed with what is called a metric. This book deals with this. – Idris Addou May 17 '15 at 23:49
In this book you do not find ''linking numbers'' nor ''helicity'' – Idris Addou May 17 '15 at 23:51
Yeah but this is a long road..I just want to learn the basucs really quickly so as I can move on to linking numbers – TheQuantumMan May 18 '15 at 00:25

Topology-book for self study about physical meaning

2 Answers2