Fall 2003–04and Topology MWF 10:00 // 159 Sloan Daniel Groves |
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Course Objective:
Math
109a is the first of three courses in the 109 sequence, and is an introduction
to topology. We start by defining topological spaces, considered in the abstract. This will
include such topics as compactness and Hausdorff spaces, some basic
constructions and a hint at the myriad pathologies in arbitrary topological
spaces. The second part of the course concerns homotopy and the fundamental
group. We will cover topics such as: the fundamental group; covering spaces;
group presentations; van Kampen's theorem. The third part covers homology (and maybe some cohomology, time permitting).
This will largely cover the definition of the simplicial and singular
homologies, with examples and applications. Along the way, we'll see such things as simplicial and cell complexes;
manifolds; and basic topological constructions such as: products, quotients,
suspensions, joins and wedges. Prerequisites: Ma 2 or
equivalent, and Ma 108 must be taken previously or concurrently. Text: Vassiliev, Introduction to Topology, 1st edition, AMS, 2001.
We will take a somewhat different approach to that of Vassiliev (with
appropriate references given for such divergence), so the assessment may cover
topics from lectures which are not in Vassiliev.
Other references supplied in first class. Grading Policy: Weekly homework (30%), a midterm (30%) and a final (40%). Homework:
Sheet 1: .pdf
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Contact:
Instructor:Daniel Groves groves@caltech.edu |