401-3001-61L Algebraic Topology I

Abstract	This is an introductory course in algebraic topology. Topics covered include: singular homology, cell complexes and cellular homology, the Eilenberg-Steenrod axioms, cohomology. Along the way we will introduce the basics of homological algebra and category theory.
Objective
Literature	1) G. Bredon, "Topology and geometry", Graduate Texts in Mathematics, 139. Springer-Verlag, 1997. 2) A. Hatcher, "Algebraic topology", Cambridge University Press, Cambridge, 2002. Book can be downloaded for free at: http://www.math.cornell.edu/~hatcher/AT/ATpage.html See also: http://www.math.cornell.edu/~hatcher/#anchor1772800 3) E. Spanier, "Algebraic topology", Springer-Verlag
Prerequisites / Notice	You should know the basics of point-set topology. Useful to have (though not absolutely necessary) basic knowledge of the fundamental group and covering spaces (at the level usually covered in the course "topology"). Some knowledge of differential geometry and differential topology is useful but not absolutely necessary. Some (elementary) group theory and algebra will also be needed.