MATH 7780, Advanced Algebraic Topology I, Fall Semester 2012
Instructor:
Krystyna Kuperberg
Office: PKH 238
Class, PKH 320: MWF, 2:00pm - 2:50pm
Office Hours, PKH 238: MWF 1:00pm-ca. 1:50pm; or by appointment
Textbook: Differential Forms in Algebraic Topology by Raoul Bott and Loring Tu
Brief notes or summaries (some links may not be active yet).
- Singular homology
- A special case of CW complexes
- Homotopy Extension Theorem
- Hurewicz Theorem
- Mayer Vietoris Sequence, part I
- de Rham complex
- Mayer Vietoris Sequence, part II
Other sources (newer editions as well as electronic versions may exist):
- Boothby, William M. (2002), An Introduction to Differentiable Manifolds and Riemannian Geometry, Second edition, Academic Press
- Eilenberg, Samuel; Steenrod, Norman (1952), Foundations of Algebraic Topology,
Princeton University Press
- Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press (no cost pdf version available at author's site)
- Hu, Sze-Tsen (1959), Homotopy Theory, Academic Press
- Munkres, James R. (1984), Elements of Algebraic Topology, Addison Wesley
- Spanier, Edwin (1966), Algebraic Topology, Springer-Verlag
- Spivak, Michael (1971), Calculus On Manifolds: A Modern Approach To Classical Theorems of Advanced Calculus, Westview Press
- Spivak, Michael (1975 +), A Comprehensive Introduction to Differential Geometry, vol 1-5, Publish or Perish