## 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