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401-3001-61L  Algebraic Topology I

SemesterHerbstsemester 2017
DozierendeW. Merry
Periodizitätjährlich wiederkehrende Veranstaltung
LehrspracheEnglisch


KurzbeschreibungThis is an introductory course in algebraic topology. Topics covered include: the fundamental group, covering spaces, singular homology, cell complexes and cellular homology and the Eilenberg-Steenrod axioms. Along the way we will introduce the basics of homological algebra and category theory.
Lernziel
SkriptI will produce full lecture notes, available on my website at

www.merry.io/algebraic-topology
Literatur"Algebraic Topology" (CUP, 2002) by Hatcher is excellent and covers all the material from both Algebraic Topology I and Algebraic Topology II. You can also download it (legally!) for free from Hatcher's webpage:

www.math.cornell.edu/%7ehatcher/AT/ATpage.html

Another classic book is Spanier's "Algebraic Topology" (Springer, 1963). This book is very dense and somewhat old-fashioned, but again covers everything you could possibly want to know on the subject.
Voraussetzungen / BesonderesYou should know the basics of point-set topology (topological spaces, and what it means for a topological space to be compact or connected, etc).

Some (very elementary) group theory and algebra will also be needed.