Algebraic Topology 1: Overview

I give an overview of the topics in algebraic topology (geometric notions, fundamental group, homology groups, cohomology groups, and homotopy groups) that we will be covering in this online course. We are following the book "Algebraic Topology" by Allen Hatcher: https://pi.math.cornell.edu/~hatcher/AT/ATpage.html Class webpages: https://people.clas.ufl.edu/henry-adams/mtg6346-f2024/ https://people.clas.ufl.edu/henry-adams/mtg6347-s2025/ Accompanying notes: https://people.clas.ufl.edu/henry-adams/files/NotesChp0-MTG6346.pdf https://people.clas.ufl.edu/henry-adams/files/NotesSec1.1Sec1.2-MTG6346.pdf https://people.clas.ufl.edu/henry-adams/files/NotesSec1.3Sec1.A-MTG6346.pdf https://people.clas.ufl.edu/henry-adams/files/NotesSec2.1a-MTG6346.pdf https://people.clas.ufl.edu/henry-adams/files/NotesSec2.1b-MTG6346.pdf https://people.clas.ufl.edu/henry-adams/files/NotesSec2.2-MTG6346.pdf https://people.clas.ufl.edu/henry-adams/files/NotesOverviewSec2.3Sec2.C-MTG6347.pdf https://people.clas.ufl.edu/henry-adams/files/NotesSec3.1-MTG6347.pdf https://people.clas.ufl.edu/henry-adams/files/NotesSec3.2-MTG6347.pdf https://people.clas.ufl.edu/henry-adams/files/NotesIntroToManifolds-MTG6347.pdf https://people.clas.ufl.edu/henry-adams/files/NotesSec3.3-MTG6347.pdf https://people.clas.ufl.edu/henry-adams/files/NotesChp4-MTG6347.pdf