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MATH 6510 — Algebraic Topology

General Information

MATH 6510-MATH 6520 are the core topology courses in the mathematics graduate program. MATH 6510 is an introductory study of certain geometric processes for associating algebraic objects such as groups to topological spaces. The most important of these are homology groups and homotopy groups, especially the first homotopy group or fundamental group, with the related notions of covering spaces and group actions. The development of homology theory focuses on verification of the Eilenberg-Steenrod axioms and on effective methods of calculation such as simplicial and cellular homology and Mayer-Vietoris sequences.

Full Cornell course description (SP26)

Credits: 4

Prerequisites and Enrollment

Prerequisites: strong performance in an undergraduate abstract algebra course at the level of MATH 4340 and point-set topology at the level of MATH 4530, or permission of instructor.

Recorded Offerings

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Course information checked against Cornell’s Spring and Fall 2026 rosters on September 18, 2026. The listed semesters are verified examples, not a complete offering history.