Algebraic Topology

Course Information
TitleΑΛΓΕΒΡΙΚΗ ΤΟΠΟΛΟΓΙΑ / Algebraic Topology
Code0672
FacultySciences
SchoolMathematics
Cycle / Level2nd / Postgraduate
Teaching PeriodSpring
CoordinatorGeorgios Raptis
CommonYes
StatusActive
Course ID40003414

Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)

Registered students: 8
OrientationAttendance TypeSemesterYearECTS
THEŌRĪTIKA MATHĪMATIKACompulsory Course2110
THEŌRĪTIKĪ PLĪROFORIKĪ KAI THEŌRIA SYSTĪMATŌN KAI ELEGCΗOUCompulsory Course2110
Class Information
Academic Year2025 – 2026
Class PeriodSpring
Faculty Instructors
Class ID
600291528
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Examination)
Course Content (Syllabus)
Homotopy and homotopy equivalence, retractions and deformation retractions. Introduction to categories. The fundamental group: basic constructions, path and homotopy lifting properties of covering spaces, fundamental group of the circle. Free product, the Seifert-van Κampen theorem. Calculations and applications, surfaces and knots. Covering spaces, lifting criterion, existence for subgroup of the FG. Homology: definition of singular homology, chain complexes. Long exact sequence of pair, homology of spheres, the Mayer-Vietoris sequence.
Student Assessment
Description
Homeworks and final exam.
Bibliography
Course Bibliography (Eudoxus)
A. Hatcher: Algebraic Topology, free on the web G. Bredon: Topology and Geometry, Springer 1993 J. Rotman: An Introduction to Algebraic Topology, Springer 1988 J. P. May: A Concise Course in Algebraic Topology, 1999 free on the web T. tom Dieck: Algebraic Topology, EMS 2008 J. Munkres: Topology (FG) and Elements of Algebraic Topology (Homology)
Last Update
24-05-2023