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Professor Alexandru I. Suciu
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MATH 4565 · Topology
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Spring 2016
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Course Information
Course Description
This course provides an introduction to the concepts and methods of Topology. It consists of two inter-connected parts.
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1. Topological Spaces and Continuous Maps
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This part of the course serves as an introduction to General Topology. The objects of study are topological spaces and continuous maps between them. Key is the notion of homeomorphism, which leads to the study of topological invariants. The main properties that are studied are connectedness, path connectedness, and compactness, as well as their "local" versions. We also introduce several constructions of spaces, including identification spaces.
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2. Fundamental Group and Covering Spaces
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This part of the course is a brief introduction to Geometric Topology. It starts with Poincaré's definition of the fundamental group of a space, and various methods to compute it, such as the Seifert-van Kampen theorem. It proceeds with the classification of surfaces, and a detailed study of covering spaces. Applications include the Brouwer fixed point theorem, the Borsuk-Ulam theorem, and the Nielsen-Schreier theorem.
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Homework Assignments
Assignment
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Chapter
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Page
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Problems
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Homework 1
Due Jan. 27
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Munkres 2.13
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83
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3
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Munkres 2.16
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91-92
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1, 4, 5
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Munkres 2.18
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111-112
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3, 10
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Homework 2
Due Feb. 3
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Munkres 2.17
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100-102
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2&3, 6, 11&12, 13, 14
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Munkres 2.20
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126
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3
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Homework 3
Due Feb. 17
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Munkres 3.23
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152
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4, 6, 9
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Munkres 3.24
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158
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8, 9, 10
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Homework 4
Due Feb 29
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Munkres 3.24
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158
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2, 3
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Munkres 3.25
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162
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4, 5(a), 6, 7
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Homework 5
Due March 30
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Munkres 2.22
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145
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3
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Munkres 2.22 supplement
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146
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4, 5(a)-(c)
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Munkres 3.26
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172
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12, 13(a)-(b)
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Munkres 9.51
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330
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3(c)(d)
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Homework 6
Due April 11
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Munkres 9.52
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335
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3, 6
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Munkres 9.53
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341
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3, 4, 6(b)
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Munkres 9.58
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366
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5&6
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Handouts
Exams
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