Regular solids and isolated singularities (Advanced Lectures in Mathematics) - Tapa blanda

Lamotke, Klaus

 
9783528089580: Regular solids and isolated singularities (Advanced Lectures in Mathematics)
Tapa blanda
ISBN 10: 352808958X ISBN 13: 9783528089580
Editorial: Springer, 2013

Sinopsis

The last book XIII of Euclid’s Elements deals with the regular solids which therefore are sometimes considered as crown of classical geometry. More than two thousand years later around 1850 Schl~fli extended the classification of regular solids to four and more dimensions. A few decades later, thanks to the invention of group and invariant theory the old three­ dimensional regular solid were involved in the development of new mathematical ideas: F. Klein (Lectures on the Icosa­ hedron and the Resolution of Equations of Degree Five, 1884) emphasized the relation of the regular solids to the finite rotation groups. He introduced complex coordinates and by means of invariant theory associated polynomial equations with these groups. These equations in turn describe isolated singularities of complex surfaces. The structure of the singularities is investigated by methods of commutative algebra, algebraic and complex analytic geometry, differential and algebraic topology. A paper by DuVal from 1934 (see the References), in which resolutions play an important rele, marked an early stage of these investigations. Around 1970 Klein’s polynomials were again related to new mathematical ideas: V. I. Arnold established a hierarchy of critical points of functions in several variables according to growing com­ plexity. In this hierarchy Kleinls polynomials describe the "simple" critical points.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

The last book XIII of Euclid's Elements deals with the regular solids which therefore are sometimes considered as crown of classical geometry. More than two thousand years later around 1850 Schl~fli extended the classification of regular solids to four and more dimensions. A few decades later, thanks to the invention of group and invariant theory the old three­ dimensional regular solid were involved in the development of new mathematical ideas: F. Klein (Lectures on the Icosa­ hedron and the Resolution of Equations of Degree Five, 1884) emphasized the relation of the regular solids to the finite rotation groups. He introduced complex coordinates and by means of invariant theory associated polynomial equations with these groups. These equations in turn describe isolated singularities of complex surfaces. The structure of the singularities is investigated by methods of commutative algebra, algebraic and complex analytic geometry, differential and algebraic topology. A paper by DuVal from 1934 (see the References), in which resolutions play an important rele, marked an early stage of these investigations. Around 1970 Klein's polynomials were again related to new mathematical ideas: V. I. Arnold established a hierarchy of critical points of functions in several variables according to growing com­ plexity. In this hierarchy Kleinls polynomials describe the "simple" critical points.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2013
Idioma
Alemán
ISBN 10 
352808958X
ISBN 13 
9783528089580
Encuadernación
Tapa blanda
Número de páginas
236
Contacto del fabricante
no disponible
Persona responsable
no disponible