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MATH-497: Topology IV.b - homotopy theory

Summary

We propose an introduction to homotopy theory for topological spaces. We define higher homotopy groups and relate them to homology groups. We introduce (co)fibration sequences, loop spaces, and suspensions. We study long exact sequences. We construct Eilenberg-Mac Lane spaces.

Lectures

Instructor

Jérôme Scherer

Official source

https://edu.epfl.ch/coursebook/en/topology-iv-b-homotopy-theory-MATH-497

Moodle Page

http://go.epfl.ch/MATH-497

About this result

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Summary

Lectures

Instructor

Jérôme Scherer

Official source

https://edu.epfl.ch/coursebook/en/topology-iv-b-homotopy-theory-MATH-497

Moodle Page

http://go.epfl.ch/MATH-497

About this result

Ontological neighbourhood

Mathematics

Topology: Algebraic topology

Lectures in this course (27)

Introduction to Topology

Covers fundamental concepts of space, topology, groups, and homology theory.

Compact-open topology

Covers the compact-open topology, defining maps between spaces and discussing continuous maps and preimages in topology.

Cellular Approximation: Homotopy and CW Complexes

Explores the cellular approximation theorem for CW complexes and its implications on homotopy groups.

CW Approximation Theorem

Explores the CW Approximation Theorem, constructing CW complexes from spaces to ensure isomorphism on homology groups.

Mapping Cylinders and Mapping Cones

Explores mapping cylinders and cones, key in exact sequences and topology.

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