Author | Kinsey, L. Christine. author |
---|---|
Title | Topology of Surfaces [electronic resource] / by L. Christine Kinsey |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0899-0 |
Descript | X, 281 p. online resource |
1. Introduction to topology -- 1.1. An overview -- 2. Point-set topology in ?n -- 2.1. Open and closed sets in ?n -- 2.2. Relative neighborhoods -- 2.3. Continuity -- 2.4. Compact sets -- 2.5. Connected sets -- 2.6. Applications -- 3. Point-set topology -- 3.1. Open sets and neighborhoods -- 3.2. Continuity, connectedness, and compactness -- 3.3. Separation axioms -- 3.4. Product spaces -- 3.5. Quotient spaces -- 4. Surfaces -- 4.1. Examples of complexes -- 4.2. Cell complexes -- 4.3. Surfaces -- 4.4. Triangulations -- 4.5. Classification of surfaces -- 4.6. Surfaces with boundary -- 5. The euler characteristic -- 5.1. Topological invariants -- 5.2. Graphs and trees -- 5.3. The euler characteristic and the sphere -- 5.4. The euler characteristic and surfaces -- 5.5. Map-coloring problems -- 5.6. Graphs revisited -- 6. Homology -- 6.1. The algebra of chains -- 6.2. Simplicial complexes -- 6.3. Homology -- 6.4. More computations -- 6.5. Betti numbers and the euler characteristic -- 7. Cellular functions -- 7.1. Cellular functions -- 7.2. Homology and cellular functions -- 7.3. Examples -- 7.4. Covering spaces -- 8. Invariance of homology -- 8.1. Invariance of homology for surfaces -- 8.2. The Simplicial Approximation Theorem -- 9. Homotopy -- 9.1. Homotopy and homology -- 9.2. The fundamental group -- 10. Miscellany -- 10.1. Applications -- 10.2. The Jordan Curve Theorem -- 10.3. 3-manifolds -- 11. Topology and calculus -- 11.1. Vector fields and differential equations in ?n -- 11.2. Differentiable manifolds -- 11.3. Vector fields on manifolds -- 11.4. Integration on manifolds -- Appendix: Groups -- References