By Francis Bonahon
The learn of three-d areas brings jointly components from numerous parts of arithmetic. the main impressive are topology and geometry, yet parts of quantity concept and research additionally make appearances. some time past 30 years, there were remarkable advancements within the arithmetic of three-dimensional manifolds. This ebook goals to introduce undergraduate scholars to a few of those very important advancements. Low-Dimensional Geometry starts off at a comparatively ordinary point, and its early chapters can be utilized as a short advent to hyperbolic geometry. despite the fact that, the final word objective is to explain the very lately accomplished geometrization software for third-dimensional manifolds. the adventure to arrive this target emphasizes examples and urban structures as an creation to extra basic statements. This comprises the tessellations linked to the method of gluing jointly the perimeters of a polygon. Bending a few of these tessellations offers a average advent to three-dimensional hyperbolic geometry and to the speculation of kleinian teams, and it will definitely ends up in a dialogue of the geometrization theorems for knot enhances and three-d manifolds. This e-book is illustrated with many photographs, because the writer meant to proportion his personal enthusiasm for the wonderful thing about the various mathematical items concerned. despite the fact that, it additionally emphasizes mathematical rigor and, aside from the latest learn breakthroughs, its buildings and statements are conscientiously justified.