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Created by:
Last updated:
November 7, 2022
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
This is a course on the singular homology of topological spaces.
Topics include: Singular homology, CW complexes, Homological algebra, Cohomology, and Poincare duality.
Course Curriculum
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- Introduction: Singular Simplices and Chains Unlimited
- Homology Unlimited
- Categories, Functors, Natural Transformations Unlimited
- Categorical Language Unlimited
- Homotopy, Star-shaped Regions Unlimited
- Homotopy Invariance of Homology Unlimited
- Homology Cross Product Unlimited
- Relative Homology Unlimited
- The Homology Long Exact Sequence Unlimited
- Excision and Applications Unlimited
- The Eilenberg Steenrod Axioms and the Locality Principle Unlimited
- Subdivision Unlimited
- Proof of the Locality Principle Unlimited
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- CW-Complexes Unlimited
- CW-Complexes II Unlimited
- Homology of CW-Complexes Unlimited
- Real Projective Space Unlimited
- Euler Characteristic and Homology Approximation Unlimited
- Coefficients Unlimited
- Tensor Product Unlimited
- Tensor and Tor Unlimited
- The Fundamental Theorem of Homological Algebra Unlimited
- Hom and Lim Unlimited
- Universal Coefficient Theorem Unlimited
- Künneth and Eilenberg-Zilber Unlimited
- Coproducts, Cohomology Unlimited
- Ext and UCT Unlimited
- Products in Cohomology Unlimited
- Cup Product (cont.) Unlimited
- Surfaces and Nondegenerate Symmetric Bilinear Forms Unlimited
- Local Coefficients and Orientations Unlimited
- Proof of the Orientation Theorem Unlimited
- A Plethora of Products Unlimited
- Cap Product and “Cech” Cohomology Unlimited
- Cech Cohomology as a Cohomology Theory Unlimited
- The Fully Relative Cap Product Unlimited
- Poincaré Duality Unlimited
- Applications Unlimited
About the instructor
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Massachusetts Institute of Technology
