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401-3001-61L  Algebraic Topology I

SemesterAutumn Semester 2018
LecturersP. Biran
Periodicityyearly recurring course
Language of instructionEnglish


AbstractThis 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
Literature1) 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 / NoticeYou 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.