Algebraic Topology

A.A. 2022-2023

Teacher: LUCIA CAPORASO - Office hours: Tuesday 16-18 - Thursday 18-19 by appointment

Room: 111 - Ph: 06 5733 8040 - E-mail: caporaso--at--mat.uniroma3.it

Topics (not in chronological order):

  • Classification of covering spaces via the fundamental group.
  • Categories.
  • Abstract and geometric complexes.
  • Singular and simplicial homology.
  • Cohomology.
  • Duality theorems .
  • Persistent homology and topological data analysis.

    Textbooks.

  • Allen Hatcher: Algebraic topology Cambridge University press.
  • Lucia Caporaso : Lezioni di topologia
  • James R. Munkres : Topology Prentice Hall.
  • Vidit Nanda: Computational Algebraic Topology - Lecture notes

    Lectures : Tuesday 14-16, Thursday 16-18 Room M4

    First lecture: Tuesday Sept. 20, 14-16. Room M6.

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