Algebraic topology

Mathematics BSc
Course description
2013.

Eötvös Loránd University
Faculty of Science
Institute of Mathematics

Borromean Rings

All courses
Core courses
- Algebra, number theory
- Analysis
- Geometry
  - Geometry 1
- Discrete mathematics
  - Discrete mathematics 1
  - Discrete mathematics 2
- Elementary mathematics
  - Elementary mathematics 1
- Informatics
  - Prog. fundamentals
Pure mathematics
- Algebra, number theory
- Analysis
  - Analysis 3
  - Analysis 4
  - Applied analysis
    - Numerical analysis
    - Appl. anal. comp.
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Topology
    - Introduction
    - Algebraic topology
  - Complex analysis
  - Functional analysis
  - Function series
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Informatics
- Computer science
- Foundations of math.
  - Set theory
  - Mathematical logic
Applied mathematics
- Analysis
  - Analysis 3
  - Analysis 4
  - Analysis 5
  - Applied analysis
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Complex analysis
  - Functional analysis
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Applied modules
- Informatics
- Algorithms
- Algebra
- Elementary mathematics
  - Elementary mathematics 2
  - Elementary mathematics 3
- Foundations of math.
BSc: general information
Studies

Algebraic topology

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
2 + 2	2 + 3	exam + term grade	pure math.	mm1c1to4m mm1c2to4m	4	optional

Course coordinator

András Szűcs
Department of Analysis
Institute of Mathematics

Strong	Weak	Prerequisites
Practice class
Practice class		Strong: Introduction to topologyL-p (mm1c1to3m)
Lecture
Lecture		Weak: practice class

Remarks

Syllabus designed by:

András Szűcs, Department of Analysis, Institute of Mathematics.

Literature

Recommended:

W. S. Massey: Algebraic Topology: An Introduction. Yale 1971.
J. W. Milnor: Topology from the differentiable viewpoint. Virginia 1965.

Syllabus

Homotopic equivalence. Van Kampen theorem. The fundamental group of torical knots. CW complexes and their fundamental groups. Canonical surfaces and their fundamental groups. Topological manifolds. Classification of 1-dimensional manifolds. Classification of closed surfaces. The Euler characteristics. The fundamental groups of manifolds admitting dimension at least four.
The Poincaré hypothesis. Differentiable manifolds.
Borsuk-Ulam and Brouwer theorems in n dimension. The degree. The Poincaré-Hopf theorem.