The zeroth homotopy group classifies domain walls. The third homotopy group, applied to defects in three-dimensional materials, classifies what the condensed matter people call textures and the particle people sometimes call skyrmions. The fourth homotopy group, applied to defects in space-time path integrals, classifies types of instantons.

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Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).