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Course Details for A.Y. 2016/2017

The information on this page refer to the academic year 2016/2017. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2016/2017

Name:

Geometria Superiore 1 / Advanced Geometry 1

Type:

Module

Main course:

Geometria Superiore / Advanced Geometry

Basic information

Code:

DT0118

Sector:

MAT/03

Credits:

: Master Degree in Mathematics 6 CFU (b)

Term:

1^st semester

Degree(s):

Master Degree in Mathematics 1^st anno curriculum Generale Compulsory

Language:

English

Teacher(s):

Aldo Biancofiore

Course Content

DIFFERENTIABLE VARIETIES. Definitions. Examples of differentiable varieties. Differentiable functions. Differentiable maps. Tangent space. Cotangent Space. More examples of differentiable varieties. Subvarieties. Paracompactness and partition of unity. Whitney’s Theorem.
GROUP ACTIONS. Topological groups and Lie groups. Homomorphisms of Lie groups. Groups actions. The action of a discrete group on a variety. Homogeneous Spaces. Examples of homogeneous spaces. Connected Lie groups. Grassmann variety. Flag variety.
DE RHAM COHOMOLOGY. Multilinear Algebra recalls. Tangent and cotangent bundles. Differential forms. De Rham cohomology. Poincaré’s Lemma. Hypersurfaces and fields of normal vectors. Orientable manifolds. Mayer-Vietoris’ sequence and its application in computing De Rham cohomology.

Assessment Methods and Criteria

Esame orale

Course page updates

This course page is available (with possible updates) also for the following academic years:

To read the current information on this course, if it is still available, go to the university course catalogue .

Course information last updated on: 15 marzo 2016, 22:41

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