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Math 643

Dr. Paulo Lima-Filho

Course Information and Policies
Your instructor:
  • Name : Dr. Paulo Lima-Filho
    E-mail : plfilho@math.tamu.edu
    Office : Milner Hall, Room 306
    URL : http://www.math.tamu.edu/~Paulo.Lima-Filho
    Phone : 845-5298 (office)
    • Primary Reference:
    Algebraic Topology, a first course, by Marvin J. Greenberg and John R. Harper. (Since this book is currently unavailable in bookstores, copies may be purchased at Copy Corner.)
    Brief course description:
    This is the first part of a one-year introduction to Algebraic Topology. The material covered during this semester can be roughly divided into three parts:
  • Part I: Singular homology theory. Here we introduce singular homology theory on arbitrary topological spaces and prove its main properties, which comprise the Eilenberg-Steenrod Axioms. Then we study special spaces such as spherical and cell complexes and the Mayer-Vietoris exact sequence, along with various immediate applications.
  • Part II: Duality in Manifolds. Here we introduce singular cohomology theory and prove its basic properties. Then we study the cup and cap products and orientation on manifolds. Finally, we prove the various important duality theorems due to Poincar\'e, Alexander and Lefschetz.
  • Part III: Products and Lefschetz fixed point theory. Here we study products of spaces, the Kunneth formula and the Universal Coefficients theorem. The course ends with the Lefschetz fixed point theorem and applications.
    • Schedule of classes:
  • Section 600 : Lectures : ENPH 214 -- MWF 3:00pm - 3:50pm
    • Grading policies: The grading for the course will be based on the following activities: one take-home Exam; one Final Exam; various assignments.
    Exam: Given on October 14, 1998. Worth 100 points.
    Final Exam: Worth 200 points.
    Assignments: Evenly distributed along the course, they will total 100 points.
  • Grading: The total number of points will add up to 400, and the grading will follow standard distribution.
    • Office Hours
    are held on Mondays, Wednesdays and Fridays in my office, from 12:30pm to 1:30pm, or by appointment. Please make thorough use of them.
    Policy on Academic Dishonesty:
    All exams are activities to be performed individually by each student. Any violation of this policy or any cases of scholastic dishonesty will have severe and undesirable consequences for the perpetrators.
    Makeup Exams:
    will be given only in case of an absence authorized under University Regulations (Section 15 thereof). A note from your doctor or academic advisor is necessary. If you know in advance that you will miss an exam, please contact me beforehand, via e-mail.
    Miscellaneous notes:
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