Посилання:Homotopy in statistical physics / R. Kenna // Condensed Matter Physics. — 2006. — Т. 9, № 2(46). — С. 283–304. — Бібліогр.: 74 назв. — англ.
Підтримка:The author wishes to thank Bertrand Berche, Arnaldo Donoso and Ricardo Paredes for their
organizing the Mochima Spring School. The remaining participants, and in particular the students,
are also thanked for making the School so dynamic and interesting. The author further thanks
Dominique Mouhanna and Aernout van Enter for enlightening comments.
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.