دانلود کتاب Surface topology

1: Intuitive Ideas. 1.1: Introduction. 1.2: Preliminary skirmish. 1.3: Models. 1.4: Connected sets. 1.5: Problem surfaces. 1.6: Homeomorphic surfaces. 1.7: Some basic surfaces. 1.8: Orientability. 1.9: The connected sum construction. 1.10: Summary. 1.11: Exercises -- 2: Plane Models of Surfaces. 2.1: The basic plane models. 2.2: Paper models of the basic surfaces. 2.3: Plane models and orientability. 2.4: Connected sums of the basic surfaces. 2.5: Summary. 2.6: Comments. 2.7: Exercises -- 3: Surfaces as Plane Diagrams. 3.1: Plane models and the connected sum construction. 3.2: Algebraic description of surfaces. 3.3: Orientable 2n-gons. 3.4: Non-orientable 2n-gons. 3.5: The working definition of a surface. 3.6: The classification theorem. 3.7: Summary. 3.8: Exercises -- 4: Distinguishing Surfaces. 4.1: Introducing [actual symbols not reproducible] (M). 4.2: [actual symbols not reproducible] (M) and the connected sum construction. 4.3: How to tell the difference. 4.4: Can you tell the difference? 4.5: Comments. 4.6: Exercises -- 5: Patterns on Surfaces. 5.1: Patterns and [actual symbols not reproducible] (M). 5.2: Complexes. 5.3: Regular complexes. 5.4: b-Valent complexes. 5.5: Comments. 5.6: Exercises -- 6: Maps and Graphs. 6.1: Colouring maps on surfaces. 6.2: Embedding graphs in surfaces. 6.3: Planar graphs. 6.4: Outerplanar graphs. 6.5: Embedding the complete graphs. 6.6: Sprouts. 6.7: Brussels sprouts. 6.8: Comments. 6.9: Exercises -- 7: Vector Fields on Surfaces. 7.1: A water proof. 7.2: Hairy surfaces. 7.3: Interpretations of the index theorem. 7.4: Lakes. 7.5: Islands in lakes. 7.6: Islands. 7.7: Vector fields and differential equations. 7.8: Comments. 7.9: Exercises -- 8: Plane Tessellation Representations of Compact Surfaces. 8.1: Plane Euclidean geometry. 8.2: Groups. 8.3: Plane hyperbolic geometry. 8.4: Plane tessellations. 8.5: Comments. 8.6: Exercises -- 9: Some Applications of Tessellation Representations. 9.1: Introduction. 9.2: Tessellations and patterns. 9.3: Tessellations and map colouring. 9.4: Tessellations and vector fields. 9.5: Summary. 9.6: Exercises -- 10: Introducing the Fundamental Group. 10.1: Introduction. 10.2: The fundamental group. 10.3: Isomorphic groups. 10.4: Comments. 10.5: Exercises