Low-Dimensional Geometry: From Euclidean Surfaces to by Francis Bonahon

By Francis Bonahon

The examine of third-dimensional areas brings jointly components from numerous components of arithmetic. the main outstanding are topology and geometry, yet parts of quantity thought and research additionally make appearances. long ago 30 years, there were awesome advancements within the arithmetic of three-d manifolds. This publication goals to introduce undergraduate scholars to a few of those very important advancements. Low-Dimensional Geometry begins at a comparatively user-friendly point, and its early chapters can be utilized as a quick creation to hyperbolic geometry. despite the fact that, the final word aim is to explain the very lately accomplished geometrization application for three-d manifolds. the adventure to arrive this objective emphasizes examples and urban structures as an creation to extra common statements. This comprises the tessellations linked to the method of gluing jointly the edges of a polygon. Bending a few of these tessellations offers a usual advent to third-dimensional hyperbolic geometry and to the speculation of kleinian teams, and it will definitely results in a dialogue of the geometrization theorems for knot enhances and third-dimensional manifolds. This publication is illustrated with many images, because the writer meant to proportion his personal enthusiasm for the great thing about a number of the mathematical gadgets concerned. even though, it additionally emphasizes mathematical rigor and, except for the newest examine breakthroughs, its buildings and statements are conscientiously justified.

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Poisson-Geometrie und Deformationsquantisierung: Eine by Stefan Waldmann

By Stefan Waldmann

In diesem Buch werden die Grundlagen der Poisson-Geometrie und der Deformationsquantisierung ausgehend von physikalischen Fragestellungen auf kohärente Weise entwickelt. Die Poisson-Geometrie bietet einen allgemeinen Rahmen für die geometrische Mechanik und stellt eine Verallgemeinerung der symplektischen Geometrie dar. Diese nimmt, insbesondere im Hinblick auf mechanische Systeme mit Symmetrien und deren Phasenraumreduktion, einen wichtigen Platz ein. Für die angestrebte Quantisierung werden die geometrischen Sachverhalte algebraisch gedeutet und entsprechend formuliert. Darauf aufbauend bietet die Deformationsquantisierung einen allgemeinen Rahmen für die Quantisierung von Poisson-Mannigfaltigkeiten, der nun erstmals in Lehrbuchform entwickelt wird. Zentrale Themen wie die Fedosov-Konstruktion von Sternprodukten sowie Elemente der Darstellungstheorie der deformierten Algebren werden im element vorgestellt. Ausführliche Beweise und über a hundred Übungsaufgaben mit Lösungshinweisen erleichtern ein Selbststudium.

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Topological Topics: Articles on Algebra and Topology by I. M. James

By I. M. James

Professor Peter Hilton is among the most sensible identified mathematicians of his iteration. He has released virtually three hundred books and papers on numerous points of topology and algebra. the current quantity is to have a good time the social gathering of his 60th birthday. It starts off with a bibliography of his paintings, by means of reports of his contributions to topology and algebra. those are by means of 11 study papers eager about quite a few issues of present curiosity in algebra and topology. The articles are contributed by means of a few of the many mathematicians with whom he has labored at one time or one other. This e-book might be of curiosity to either topologists and algebraists, rather these excited about homotopy thought.

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Differential Topology: Proceedings of the Second Topology by Hugh M. Hilden, Maria Teresa Lozano, José Maria Montesinos

By Hugh M. Hilden, Maria Teresa Lozano, José Maria Montesinos (auth.), Ulrich Koschorke (eds.)

The major matters of the Siegen Topology Symposium are mirrored during this number of sixteen study and expository papers. They focus on differential topology and, extra in particular, round linking phenomena in three, four and better dimensions, tangent fields, immersions and different vector package morphisms. Manifold different types, K-theory and crew activities also are discussed.

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