In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction to the mathematical methods involved in topology and homotopy theory, the role of the latter in a number of mainly low-dimensional statistical-mechanical systems is outlined. Some recent activities in this area are reviewed and some possible future directions are discussed.
Bibliographical noteThe full text is available from: http://dx.doi.org/10.5488/CMP.9.2.283
- phase transitions
- topological defects