Course Description:
Continues MTH G121. Introduces homology and cohomology theory. Studies singular homology, homological algebra (exact sequences, axioms), Mayer-Vietoris sequence, CW-complexes and cellular homology, calculation of homology of cellular spaces, and homology with coefficients. Moves on to cohomology theory, universal coefficients theorems, Bockstein homomorphism, Knnneth formula, cup and cap products, Hopf invariant, Borsuk-Ulam theorem, and Brouwer and Lefschetz-Hopf fixed-point theorems. Ends with a study of duality in manifolds including orientation bundle, Poincaré duality, Lefschetz duality, Alexander duality, Euler class, Lefschetz numbers, Gysin sequence, intersection form, and signature.
Fall Offering:
None
Lab/Coreq 1:
Spring Offering:
None
Lab/Coreq 2:
Summer Offering:
None
Lab/Coreq Remarks:
Summer 1 Offering:
None
Prerequisite 1:
MTH G112
Summer 2 Offering:
None
Prerequisite 2:
MTH G121
Cross-Listed Course 1:
Prerequisite 3:
Cross-Listed Course 2:
Prerequisite 4:
Cross-Listed Course 3:
Prerequisite 5:
Cross-Listed Course 4:
Prerequisite Remarks:
Cross-Listed Course 5:
Repeatable:
N
