Geometric group theory
Geometric group theory, as a distinct area, is relatively new, and became a clearly identifiable branch of mathematics in the late 1980s and early 1990s.In this sense the study of geometric group theory is a part of culture, and reminds me of several things that Georges de Rham practiced on many occasions, such as teaching mathematics, reciting Mallarmé, or greeting a friend".In the first half of the 20th century, pioneering work of Max Dehn, Jakob Nielsen, Kurt Reidemeister and Otto Schreier, J. H. C. Whitehead, Egbert van Kampen, amongst others, introduced some topological and geometric ideas into the study of discrete groups.Small cancellation theory was introduced by Martin Grindlinger in the 1960s[4][5] and further developed by Roger Lyndon and Paul Schupp.The emergence of geometric group theory as a distinct area of mathematics is usually traced to the late 1980s and early 1990s.
Cayley graphfree grouphyperbolic groupGromov boundaryCantor setmathematicsfinitely generated groupsalgebraicgroupstopologicalgeometricCayley graphsmetric spaceword metriclow-dimensional topologyhyperbolic geometryalgebraic topologycomputational group theorydifferential geometrycomplexity theorymathematical logicLie groupsdynamical systemsprobability theoryK-theoryGeorges de RhamMallarmécombinatorial group theorydiscrete groupsgroup presentationsquotientsfree groupsWalther von DyckFelix Kleinicosian calculusWilliam Rowan Hamiltonicosahedral symmetrydodecahedronmeasure-theoreticMax DehnJakob NielsenKurt ReidemeisterOtto SchreierJ. H. C. WhiteheadEgbert van Kampensmall cancellation theoryBass–Serre theoryRoger LyndonPaul Schuppvan Kampen diagramssimplicial treesMostow's rigidity theoremKleinian groupsWilliam ThurstonGeometrization programMikhail GromovGromovquasi-isometrygrowth rateDehn functionfinitely presented grouphyperbolicity of a grouphomeomorphismasymptotic conesamenabilityabeliannilpotentfinitely presentableWord ProblemGromov's polynomial growth theoremStallings' ends theoremMostow rigidity theoremSchwartzBenson FarbBaumslag–Solitar groupsword-hyperbolicrelatively hyperbolicZlil Selaisomorphism problemBrian BowditchOlga Kharlampovichnon-commutative algebraic geometryautomatic groupsEliyahu RipsMark SapirJSJ-decompositions3-manifoldsgeometric analysisC*-algebrasNovikov conjectureBaum–Connes conjectureHilbert spacesCannon's conjectureFinite subdivision rulestopological dynamicsconvergence group
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