Theoretical / proof-based
Algebraic topology · Graduate · Math
Topics
Homotopy and fundamental group
- Homotopy of maps; homotopy equivalence
- Fundamental group: computation for CW complexes and surfaces
- Covering spaces and Galois correspondence
- Seifert–van Kampen theorem
- Applications to fixed-point and Brouwer theorems (introduction)
Homology theory
- Singular homology: definitions and functoriality
- Eilenberg–Steenrod axioms (overview)
- Mayer–Vietoris sequence and long exact sequences
- Cellular homology and computations for CW complexes
- Degree theory and invariance of domain (introduction)
Cohomology and duality
- Singular cohomology and universal coefficient theorem (statement)
- Cup product and ring structure on cohomology
- Poincaré duality for closed oriented manifolds
- Künneth formula (introduction)
- Introduction to spectral sequences (optional)
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$1,162 · Algebraic topology · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.