By Francis Bonahon
The research of third-dimensional areas brings jointly components from numerous parts of arithmetic. the main striking are topology and geometry, yet components of quantity thought and research additionally make appearances. long ago 30 years, there were awesome advancements within the arithmetic of third-dimensional manifolds. This e-book goals to introduce undergraduate scholars to a few of those vital advancements. Low-Dimensional Geometry starts off at a comparatively user-friendly point, and its early chapters can be utilized as a short creation to hyperbolic geometry. despite the fact that, the last 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 advent to extra normal 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 traditional creation to third-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-dimensional manifolds. This publication is illustrated with many photographs, because the writer meant to proportion his personal enthusiasm for the great thing about a few of the mathematical gadgets concerned. even though, it additionally emphasizes mathematical rigor and, apart from the newest examine breakthroughs, its structures and statements are conscientiously justified.