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Course:
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MTH 3481 -- Topology 3 (key # 15687)
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Web site:
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http://www.math.neu.edu/~suciu/mth3481/top3.sp03.html
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Instructor:
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Prof. Alex Suciu < alexsuciu@neu.edu >
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Time and Place:
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Tue. & Th., 5:30 - 7:00 PM, in 544 Nightingale
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Office Hours:
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Tue. & Th., 4:30 - 5:30 PM, or by appointment, in 441 Lake
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Prerequisites:
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MTH 3105 (Topology 1) and MTH 3107 (Topology 2)
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Textbook:
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Algebraic Topology, by Allen Hatcher, Cambridge University Press, 2002. Download here.
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Supplement:
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Topology and Geometry, by Glen Bredon, Springer-Verlag, GTM #139, 1997.
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Grade:
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Based on problem sets, a final exam, and class participation.
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This course is an introduction to cohomology theory, duality in manifolds, and homotopy theory. We will cover a (proper!) subset of the following list of topics.
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Cohomology Theory
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Cohomology of chain complexes, simplicial, singular and cellular cohomology, homology and cohomology with coefficients, transfer homomorphism, universal coefficients theorems, cup product, cohomology ring, cross product, Künneth formula, H-spaces and Hopf algebras, Bockstein homomorphism.
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Duality in Manifolds
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The orientation bundle, cap product, Poincaré duality, Lefschetz duality, Alexander duality, Euler class, Gysin sequence, cobordism, intersection form, signature, plumbing.
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Homotopy Theory
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Higher homotopy groups, cofibrations, fibrations, homotopy sequences, homotopy groups of Lie groups and associated manifolds, cellular approximation, Hurewicz theorem, Whitehead theorem, Eilenberg-MacLane spaces, obstruction theory.
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Course Information 
alexsuciu@neu.edu
