2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51899Symmetry breaking can produce ``Alice'' strings, which alter scattered charges and carry monopole number and charge when twisted into loops. Alice behavior arises algebraically, when a string's untraced Wilson loop obstructs unbroken symmetries -- a fragile criterion. We give a topological criterion, compelling Alice behavior or deforming it away. Our criterion, that π_o(H) acts nontrivially on π_1(H), links topologically Alice strings to topological monopoles. We twist Alice loops to form monopoles, and find nematic and He-3A Alice strings are topologically Alice, carrying fundamental monopole charge when twisted into loops.12 pages, 1 figure, text + 2 eps files submitted 4/17/03, revised 12/5/03: technical qualification added, introduction focused, nomenclature clarifiedHigh Energy Physics - TheorySoft Condensed Mattertext