Università di Pavia - Offerta formativa

TOPICS IN GEOMETRY

Enrollment year

2018/2019

Academic year

2020/2021

Regulations

DM270

Academic discipline

MAT/03 (GEOMETRY)

Department

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

Course

MATHEMATICS

Curriculum

PERCORSO COMUNE

Year of study

3°

Period

1st semester (01/10/2020 - 20/01/2021)

ECTS

6

Lesson hours

56 lesson hours

Language

Italian

Activity type

WRITTEN AND ORAL TEST

Teacher

PERNAZZA LUDOVICO (titolare) - 6 ECTS

Prerequisites

The basic notions of group theory, linear algebra and general topology.

Learning outcomes

An introduction to homotopy and homology

Course contents

The fundamental group. Free groups. The theorems of Van Kampen.

Covering spaces.

Basic notions of homological algebra. Singular homology and its homotopic properties, relative homology, axiomatic homology theory. Simplicial complexes, CW-complexes. Triangulations, Euler-PoincarĂ¨ characteristic, orientation, the classification of surfaces. Jordan curve theorem, invariance of domain.

Covering spaces.

Basic notions of homological algebra. Singular homology and its homotopic properties, relative homology, axiomatic homology theory. Simplicial complexes, CW-complexes. Triangulations, Euler-PoincarĂ¨ characteristic, orientation, the classification of surfaces. Jordan curve theorem, invariance of domain.

Teaching methods

Lectures and problem sessions

Reccomended or required readings

A. Hatcher: "Algebraic Topology", Cambridge University Press (freely available online)

M. Greenberg, J. Harper: "Algebraic Topology".

W. Massey: "A Basic Course in Algebraic Topology", Springer-Verlag.

E. Spanier: "Algebraic Topology".

M. Greenberg, J. Harper: "Algebraic Topology".

W. Massey: "A Basic Course in Algebraic Topology", Springer-Verlag.

E. Spanier: "Algebraic Topology".

Assessment methods

Written and oral exam.

Further information

Sustainable development goals - Agenda 2030