Topics in Geometric Group TheoryUniversity of Chicago Press, 15. 9. 2000 - Počet stran: 310 In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields. |
Obsah
I | 1 |
II | 5 |
V | 7 |
VI | 17 |
VIII | 25 |
IX | 43 |
XI | 60 |
XII | 68 |
XXIII | 180 |
XXIV | 187 |
XXV | 194 |
XXVI | 197 |
XXVII | 206 |
XXVIII | 211 |
XXX | 217 |
XXXI | 225 |
XIII | 71 |
XIV | 75 |
XV | 84 |
XVI | 117 |
XVII | 135 |
XVIII | 145 |
XIX | 148 |
XX | 151 |
XXII | 167 |
XXXII | 236 |
XXXIII | 240 |
XXXIV | 248 |
XXXV | 259 |
XXXVI | 265 |
295 | |
XXXVIII | 299 |
323 | |
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abelian group Algebra Amer automorphism Baumslag-Solitar groups Cayley graph Chapter Check commensurable compact Complement Comput Consider contains Corollary countable curvature defined Definition denote discrete subgroup element example Exercise exists exponential growth finite group finite index finite kernels finite set finitely presented finitely-generated group finitely-presented group follows free group free product free subgroups fundamental group geodesic geometric Grigorchuk Gromov group G group of order group of rank group theory growth function growth series homomorphism hyperbolic groups infinite integer isometries isomorphic Item lattice Lemma Lie group London Math Lubotzky mapping metric space modular group non-abelian free normal subgroup Observe p-group particular polynomial growth proof properties Proposition quasi-isometric quotient random walks reduced word residually finite result Riemannian manifold Section simple groups SL(n solvable spherical growth subgroup of finite subset surface of genus T₁ Theorem topology torsion-free uncountably uniformly exponential growth vertex vertices