Topics in advanced topology

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Oikonomides Catherine 
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Syllabus updated
Lecture notes updated
Fall Semester  /  Recommended semester:8

Outline of lecture

Purpose of lecture

縲The aim of this course is to become familiar with the basic
concepts of homotopy theory and of singular homology theory.
The course will be given in English. An important goal of the course
is also to get used to doing mathematics in English.

Plan of lecture

1- Homotopy of paths.
2- The fundamental group of a topological space.
3- Covering spaces.
4- Singular Homology.
5- Homotopy invariance of singular homology.
6- Relative homology.
7- Exact sequences.
8- Orientation of manifolds.
9- Singular cohomology.
10- Cup and cap products.
11- Poincare duality.

Textbook and reference

Main textbook:
"Algebraic topology, a first course" (Greenberg and Harper)

Another useful reference:
"Topology" (Munkres)

Related and/or prerequisite courses


Final exam (60%), homework and class participation (40%).

Comments from lecturer

The course will be given in English, and I will do my best
to speak clearly and to make the course easy to understand.
I hope the students who take this course can make progress
in their ability to understand spoken English and to
express themselves in English during the semester.
The students are strongly encouraged to go to the library
and to find various textbooks, in English and in Japanese,
on homotopy theory and on singular homology theory, in order
to become familiar with the mathematical content of the course.

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