Course

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

Teaching & PhD PhD Students Virgile Simon Constantin Past EPFL PhD Students Samuel Lavenir Past EPFL PhD Students as codirector Kay Remo Werndli, Lyne Moser Courses Topology IV.a - Cohomology rings MATH-506 Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative algebra. We study an algebraic version, namely group cohomology, and compare both approa

Official source

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

Moodle Page

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

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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

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.

Topology Seminar: Tower Sequences and Homomorphisms

Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.

Exponential Law: Mapping Spaces and Compactness

Explores the exponential law for mapping spaces and the role of compactness in topological theory.

Pointed Mapping Spaces: Exponential Law and Adjunction

Explores pointed mapping spaces, the exponential law, adjunction properties, and homotopic classes.

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