28446 - Algebraic topology 1

Course Unit Page

  • Teacher Massimo Ferri

  • Credits 6

  • SSD MAT/03

  • Teaching Mode Traditional lectures

  • Language Italian

  • Course Timetable from Feb 20, 2019 to May 23, 2019

Academic Year 2018/2019

Learning outcomes

At the end of the course, the student knows the base elements of algebraic topology, in partucilar of homology and of the fundamental group. He/she acquires the ability of computing homology groups and fundamental group.

Course contents

Categories and functors. Simplicial complexes and delta-complexes. Homotopy. Fundamental group and edge group. Covering spaces. Singular and simplicial homology. Exact sequences. Mayer-Vietoris sequence. Orientation. CW-complexes. Classification of surfaces.

Hints at: universal coefficients, cohomology, duality; higher homotopy groups.

Readings/Bibliography

Lecture notes.

C.R.F. Maunder, "Algebraic Topology", Cambridge Univ. Press, 1980.
E.H. Spanier, "Algebraic Topology", McGraw-Hill 1966.
A. Hatcher, "Algebraic Topology", Cambridge Univ. Press, 2002. Freely downloadable.

Teaching methods

Lecture of traditional type.

Assessment methods

Oral exam, preceded by the solution of the exercises downloadable here:
http://www.dm.unibo.it/~ferri/hm/progtopalg.htm

Links to further information

http://www.dm.unibo.it/~ferri/

Office hours

See the website of Massimo Ferri