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MATH 7321 · Topology 3
Fall 2011
Tuesday 10:30-12 in 544 NI
Thursday 2:30-4:00 in 509 LA
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This is a course in classical Algebraic Topology, and some of its applications. Topics we may cover include: Higher homotopy groups, cofibrations, fibrations, fiber bundles, homotopy sequences, homotopy groups of Lie groups and associated manifolds, cellular approximation, Hurewicz theorem, Whitehead theorem, Eilenberg-MacLane spaces, obstruction theory, Postnikov towers, H-spaces and Hopf algebras, Bockstein homomorphism, Poincaré-Lefschetz duality, Alexander duality, Euler class, Gysin sequence, cobordism, intersection form, signature, plumbing, cohomology of fiber bundles, classifying spaces, characteristic classes, spectral sequences, Steenrod squares.
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We will cover material from the following textbooks:
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Algebraic Topology, by Allen Hatcher, Cambridge University Press, 2002. MR.
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Topology and Geometry, by Glen Bredon, GTM No. 139, Springer-Verlag, 1997.
MR.
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Cohomology operations and applications in homotopy theory, by Robert Mosher and Martin Tangora, Harper and Row, New York-London, 1968.
MR.
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Lecture Notes in Algebraic Topology, by James F. Davis and Paul Kirk, Graduate Studies in Mathematics, vol. 35, American Mathematical Society, Providence, RI, 2001. MR.
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Here are some other useful references, and material for further reading:
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Elements of Homotopy Theory, by George W. Whitehead, GTM No. 61, Springer-Verlag, 1979. MR.
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A user's guide to spectral sequences, by John McCleary, second edition, Cambridge Studies in Advanced Math, no. 58, Cambridge University Press, 2001. MR.
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Characteristic Classes, by John W. Milnor and James Stasheff, Ann. Math. Studies, No. 76, Princeton University Press, 1973. MR.
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Algebraic Topology, by Edwin H. Spanier, Corrected reprint, Springer-Verlag, 1981. MR.
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The topology of fibre bundles , by Norman Steenrod, reprint of 1951 edition, Princeton University Press, 1999. MR.
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Spectral Sequences in Algebraic Topology, by Allen Hatcher, draft book, 2004.
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A Concise Course in Algebraic Topology, by J. Peter May, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1999.
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 Exams
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a.suciu@neu.edu
