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Algebraic topology

    Algebraic topology

    Paths and homotopy

    We introduce the notions of path and homotopy, and give some different ways of thinking about them.

    Homotopy equivalence

    We introduce homotopy equivalence of spaces, and show that \(\mathbb R^n\) is contractible.

    Deformation retracts

    An important example of homotopy equivalence is when a space deformation retracts onto a subspace.

    Spectral sequences

    Introduction to spectral sequences

    We explain the idea behind spectral sequences, and give an example.

    Tools

    Visualizing with Grapher

    A brief tutorial in Grapher, a useful OS X program for visualizing and exploring problems in calculus and geometry.

    © Yuri Sulyma 2023