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Lecture Notes on Algebraic Topology. Jie Wu. Department of Mathematics, National University of Singapore, Singapore ,. Republic of Singapore.

**Table of contents**

- Lecture Notes
- Algebraic Topology IV: cohomology
- Your Answer
- [] Configuration spaces in algebraic topology

Contact us at: algebraictopology18 gmail. Virtual Office Hours experimental! Aim of the course This course is an introduction to Algebraic Topology. Its main topic is the study of homology groups of topological spaces.

## Lecture Notes

These homology groups provide algebraic invariants of topological spaces which can be computed in many examples of interest. In the first part of the course we will construct the singular homology groups of topological spaces and establish their basic properties, such as homotopy invariance and long exact sequences. In the second part of the course we will introduce CW-complexes. These provide a useful class of topological spaces with favorable properties, and we will explain how the homology of CW-complexes can be computed using cellular homology.

We will also discuss some basic concepts from homotopy theory. The exam is a written exam on all material treated in the course.

You are not allowed to use notes. The regular homework assignments can either be handed in by email or in person before class. Homework is optional can only increase your final grade.

The retake exam is on Wed Feb 27, in Ruppert It is optional and may be used to replace your exam grade in the above formula, if your home institution agrees. Prerequisites - Background in point-set topology: topological spaces, continuous maps, compactness, quotients and products, along the lines of these notes by A. Hatcher and maybe a first encounter with the fundamental group.

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For those who haven't seen this before, the " Intensive course on Categories and Modules" is recommended. Recordings of all the lectures will be available here , you'll need the password: Xz4F.

### Algebraic Topology IV: cohomology

Solutions to selected exercises Solutions to Selected exercises by Jorge. Solutions to Sagave's exercises week 4. Additional exercises Additional practice exercises by Jorge. Wieldberger found on youtube , and so I have had a basic foundation in some of the concepts, however this seems at a much lower level than Hatcher. This one focuses on the homology and cohomology sections of the book, and excludes the homotopy sections. I was looking for more like it, but perhaps focusing on other parts of the book?

He has course notes for a large selection of courses.

He has notes for various courses. In particular, his algebraic topology notes which don't follow Hatcher seem to be at a more elementary level:. Has lecture notes to courses he taught. In particular, there's an algebraic topology course here:. I've begun typing up notes for various things.

### Your Answer

Assuming I don't get lazy there will be a good number of things. Sign up to join this community.

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The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 3 years, 9 months ago. Active 2 years, 11 months ago.

## [] Configuration spaces in algebraic topology

Viewed 3k times. Juan Sebastian Lozano. The main points to note are that the book starts incorporating homological algebra and uses it throughout in Chapter 2, and the appendices of chapters can be skipped temporarily if you want. The last chapter in particular has a series of appendices that are very interesting and worth reading, but are almost like a survey of some more advanced idea from obstruction theory, fibrations, K-theory, etc. I might add more later as they come to mind