Uses of Homotopy theory in Condensed Matter Physics

Question

I have started to read the homotopy theory, basically from Nakahara's book. I am mainly interested in condensed matter physics. But, I don't know at the end of the day what are the problems I'll be dealing with and why I am reading it. The only way I can justify reading homotopy theory to myself is because it's beautiful math.

I'd like to know the uses of first homotopy group in condensed matter physics?

relevant: Do higher homotopy groups play any role in gauge theory?. — AccidentalFourierTransform, Oct 26 '19 at 17:43
I had already written an answer ad unfortunately the question was put on hold so I cannot post it anymore. I made the examples of statistical distributions (controlled by the fundamental group) and topological defects in topological phase transitions. — SuperCiocia, Oct 26 '19 at 18:12
I have tried to make my question more specific, if I am asked to be more specific about my question, I can't because I really don't know the uses of the homotopy group. How do I get off the hook of on hold — Galilean, Oct 26 '19 at 18:55

score 1 · Answer 1 · answered Oct 26 '19 at 18:02

One straight forward use of homotopy theory is the physics of Solitons where you try to find static,finite energy solutions to classical field theories.

You might want to read this book:

Manton, N., & Sutcliffe, P. (2004). Topological Solitons (Cambridge Monographs on Mathematical Physics). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511617034

One particular kind of soliton is the Vortex , which has been used by Abrikosov to explain some of the features of Superconductivity.

I hope it helps.

Uses of Homotopy theory in Condensed Matter Physics

1 Answers1