Homotopy groups and coverings

Homotopy groups and coverings

Abstract: This is our Bachelor's project in algebraic topology written during the fall of 93. It is aimed at students without prior knowledge of homotopy theory (like ourselves at that point of time). We define the fundamental group, covering spaces etc. and show the bijective correspondence between conjugacy classes of subgroups of the fundamental group of a space and the set of equivalence classes of connected covering spaces. We also define the higher homotopy groups and explore their (very) basic properties. Finally we include a discussion of possible algebraic structures on the set of equivalence classes of covering spaces of a given space.
All of the material apart from the last section is standard textbook material. We include a number of examples and special cases, usually only found as exercises.
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<jg@math.ku.dk>/April 8, 1997.