Singular Homology and Cohomology
Eilenberg–Steenrod axioms, cup products, and Poincaré duality.
Singular Homology and Cohomology. Eilenberg–Steenrod axioms, cup products, and Poincaré duality.
Foundations and canonical references
The standard treatments of singular homology and cohomology approach the subject from complementary angles. Hatcher, Algebraic Topology (2002) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for singular homology and cohomology include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2002Algebraic Topologyhatcher-2002
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