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.