Math 637.600
Topology II
Course Information
From the catalog: set theory, topological spaces, generalized
convergence, compactness, metrization, connectedness, uniform spaces,
function spaces.
This is the second semester of a one year course designed to provide a
modern introduction to Topology. The entire full-year course is
broadly divided into three parts: General Topology, an
introduction to Differential Topology, and an introduction to
Algebraic Topology.
In General Topology, we cover the basic notions of
topological spaces and subspaces and their basic attributes, including
a selection of these topics:
- Connectivity and connected components, spearation and
countability axioms
- Quotient spaces, nets and convergence, compactness and local
compactness, products, Tychonoff theorem, metrization theorems
- Paracompactness and basic notions in homotopy theory
In Differential Topology, we cover basic notions in the
theory of differentiable manifolds including a selection of these
topics:
- Examples, vector fields and tangent bundles
- Sard's theorem
- Immersions and submersions
- Embedding theorems
- Transversality and Pontryagin-Thom theory
In Algebraic Topology, we we study the basic notions of
algebraic techniques in topology, include a selection of these topics:
- Fundamental group and classification of covering spaces
- Homology and cohomology theories and their axioms
- CW-complexes and cellular homology
- Classical applications including the Borsuk-Ulam theorem,
Generalized Jordan curve theorem, and Lefschetz-Hopf index.
In this second semester, we will spend most of our time on algebraic
topology, but there will be applications from both general and
differntial topology.
Prerequisite: Approval of the instructor.
Jon Pitts
Office: MILN 312
Email: j-pitts@tamu.edu
URL: http://www.math.tamu.edu/~jon.pitts/
Class meets MWF 10:20-11:10 in BLOC 155.
Office hours are 11:30-12:30 (tentative) and by appointment.
Students with disabilities can get assistance from the Office of
Services for Students with Disabilities (845-1637).
Topology and Geometry by Glen E. Bredon, Graduate Texts in
Geomery 139, Springer Verlag, 1993.
Semester grades will be determined on the basis of classwork
(including both homework and class participation), (at least one)
major examination, and a final exam, all equally weighted. Problem
sets will be assigned periodically and graded. Class participation,
in the form of meaningful questions, answers, proofs, constructions,
and discussion, is required. Makeups are subject to university
policy.
Course grades will be awarded on the following basis:
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| A - Excellent performance in all aspects of the course. |
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| B - Satisfactory completion of all course requirements. |
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| C - Passing.
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A copy of this information sheet is available in
PDF format.
Created January 12, 2005. Last modified April 22, 2005.
URL: http://www.math.tamu.edu/~jon.pitts/courses/2005a/637/
Copyright ©2005 by Jon T. Pitts
