Office Hours with a Geometric Group Theorist (eBook)

Matt Clay, Dan Margalit (Herausgeber)

eBook Download: PDF

2017
456 Seiten
Princeton University Press (Verlag)
978-1-4008-8539-8 (ISBN)

Infos

Matt Clay is associate professor of mathematics at the University of Arkansas. Dan Margalit is professor of mathematics at the Georgia Institute of Technology. He is the coauthor of A Primer on Mapping Class Groups (Princeton).

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Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincare, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors.An essential primer for undergraduates making the leap to graduate work, the book begins with free groups-actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples.Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.

Produkt-Details

• Erscheint lt. Verlag: 11.7.2017
• Zusatzinfo: 136 color illus. 2 halftones. 86 line illus. 2 tables.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Sozialwissenschaften ► Pädagogik
• Schlagworte: 4-valent tree • abstract algebra • algebraic topology • Artin group • Asymptotic dimension • automorphism • automorphism group • bi-Lipschitz equivalence • bipartite graph • braid group • braids • Calculation • Cantor set • Cayley 2-complex • Cayley graph • Characterization (mathematics) • Class of groups • coarse isometry • combinatorics • Commutator subgroup • compact orientable surface • computer algebra system • Concatenation (mathematics) • cone type • Configuration space • conjugacy class • Connected component (graph theory) • Connectivity (graph theory) • Context-free Grammar • Coset • Coxeter Group • Curvature • Cycle graph (algebra) • Cyclic group • cyclic permutation • Dead End • Dehn function • Dehn twist • Diagram (category theory) • Dihedral Group • Disjoint union • Disk (mathematics) • distortion • DSV method • Eigenvalues and Eigenvectors • Endomorphism • Euclidean space • Farey complex • Farey graph • Farey tree • finite group • Finitely generated group • Floor and ceiling functions • Folding • formal language • Formal power series • free abelian group • free action • free expansion • free group • free nonabelian group • free reduction • Function (mathematics) • fundamental group • Generating set of a group • generators • geometric group theory • geometric object • geometric space • Geometry • Graph • Graph Automorphism • graph coloring • Graph (discrete mathematics) • graph isomorphism • Graph of a function • Gromov hyperbolicity • Group • group action • group element • group ends • group growth • Group (mathematics) • group presentation • group theory • Heisenberg group • Homeomorphism • Homomorphism • Homotopy • Hyperbolic Geometry • hyperbolic group • hyperbolicity • hyperbolic space • hyperplane arrangements • Identity matrix • Index • infinite graph • infinite group • Integer • integers • intersection number • Intersection number (graph theory) • Intersection (set theory) • Interval (mathematics) • isoperimetric problem • isoperimetry • jigsaw puzzle • Klein's criterion • knot theory • lamplighter group • linear algebra • line graph • manifold • Mapping class group • Mathematical Induction • Mathematical Proof • mathematical structure • Mathematics • matrix group • membership problem • Metric Space • Milnor–Schwarz lemma • Möbius transformation • Multiplication table • Neighbourhood (mathematics) • Nielsen–Schreier Subgroup theorem • non-free action • normal subgroup • number line • Number Theory • Pair of pants (mathematics) • Parity (mathematics) • path metric • Permutation • Perron–Frobenius theorem • Ping-Pong • ping-pong lemma • Planar algebra • polynomial growth theorem • Product • Proportionality (mathematics) • punctured disks • quadratic function • quasi-isometric equivalence • quasi-isometric rigidity • quasi-isometry • quasi-isometry group • quasi-isometry invariant • Quotient • reflection • reflection group • relators • residual finiteness • Riemannian Geometry • Riemannian manifold • Riemann sphere • Right angle • right-angled Artin group • Robotics • Schottky lemma • scientific notation • semidirect product • Set (mathematics) • Sign (mathematics) • simplicial complex • space • SUBGROUP • Subset • Surface • surface group • Symmetric group • symmetry • Theorem • Thompson's group • topological model • Topology • train track • Train track (mathematics) • Tree • Turing Machine • Turing's proof • Variable (mathematics) • word length • word metric • Word problem • Word problem (mathematics)
• ISBN-10: 1-4008-8539-6 / 1400885396
• ISBN-13: 978-1-4008-8539-8 / 9781400885398