Geometric Topology and Differential Geometry for Beginners (Modern Birkhäuser Classics)

The notion of a surface serves as the unifying thread that combines geometric topology and differential geometry in this distinctive text. With an abundance of illustrations, exercises, and examples, the student gains a comprehensive understanding of the relationship between the modern axiomatic approach and geometric intuition. The text maintains a concrete and motivational tone, eschewing excessive abstraction. A variety of intuitively appealing definitions and theorems regarding surfaces in the topological, polyhedral, and smooth cases are presented from a geometric perspective, while point set topology is limited to subsets of Euclidean spaces. The treatment of differential geometry is classical, focusing on surfaces in the Euclidean space R3. This material is accessible to mathematics majors at the junior or senior level.

The text's unique approach lies in its seamless integration of geometric topology and differential geometry, with the concept of a surface as the unifying thread. Numerous illustrations, exercises, and examples guide the student through the material, fostering a deep understanding of the interplay between the modern axiomatic approach and geometric intuition. The text remains grounded in concrete, motivational concepts, avoiding excessive abstraction.

From the geometric viewpoint, the reader is introduced to a range of intuitively appealing definitions and theorems concerning surfaces in the topological, polyhedral, and smooth settings. Additionally, the treatment of point set topology is confined to subsets of Euclidean spaces. The differential geometry covered in the text is classical, focusing on surfaces in the Euclidean space R3. This content is well-suited for mathematics majors at the junior or senior level.

In summary, this text offers a unique and engaging exploration of the intersection between geometric topology and differential geometry, with the notion of a surface serving as the central unifying theme. The student-friendly approach, featuring ample illustrations, exercises, and examples, ensures a rewarding learning experience for the intended audience of junior and senior-level mathematics majors.

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