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The monodromy group

Żołądek, Henryk.

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The monodromy group

Record Type:	Electronic resources : Monograph/item
Title/Author:	The monodromy group/ by Henryk Żołądek.
Author:	Żołądek, Henryk.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xvi, 687 p. :ill., digital ;24 cm.
[NT 15003449]:	Preface -- 1. Analytic Functions and Morse Theory -- 2. Normal Forms of Functions -- 3. Algebraic Topology of Manifolds -- 4. Topology and Monodromy of Functions -- 5. Integrals along Vanishing Cycles -- 6. Vector Fields and Abelian Integrals -- 7. Hodge Structures and Period Map -- 8. Linear Differential Systems -- 9. Holomorphic Foliations. Local Theory -- 10. Holomorphic Foliations. Global Aspects -- 11. The Galois Theory -- 12. Hypergeometric Functions -- Bibliography -- Index.
Contained By:	Springer Nature eBook
Subject:	Monodromy groups. -
Online resource:	https://doi.org/10.1007/978-3-031-91270-2
ISBN:	9783031912702

The monodromy group
Żołądek, Henryk.

The monodromy group[electronic resource] /by Henryk Żołądek. - Second edition. - Cham :Springer Nature Switzerland :2025. - xvi, 687 p. :ill., digital ;24 cm. - Monografie matematyczne,v. 672297-0274 ;. - Monografie matematyczne ;v. 67..

Preface -- 1. Analytic Functions and Morse Theory -- 2. Normal Forms of Functions -- 3. Algebraic Topology of Manifolds -- 4. Topology and Monodromy of Functions -- 5. Integrals along Vanishing Cycles -- 6. Vector Fields and Abelian Integrals -- 7. Hodge Structures and Period Map -- 8. Linear Differential Systems -- 9. Holomorphic Foliations. Local Theory -- 10. Holomorphic Foliations. Global Aspects -- 11. The Galois Theory -- 12. Hypergeometric Functions -- Bibliography -- Index.

This book presents the monodromy group, underlining the unifying role it plays in a variety of theories and mathematical areas. In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. In the theory of systems of linear differential equations, one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations, there appear the Ecalle-Voronin-Martinet-Ramis moduli. Moreover, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. Readers will quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature. This second edition has been enlarged by several sections, presenting new results appeared since the first edition.

ISBN: 9783031912702

Standard No.: 10.1007/978-3-031-91270-2doiSubjects--Topical Terms:

523822
Monodromy groups.

LC Class. No.: QA246 / .Z65 2025

Dewey Class. No.: 512.2

The monodromy group
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245 1 4 $a The monodromy group $h [electronic resource] / $c by Henryk Żołądek.
250 $a Second edition.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2025.
300 $a xvi, 687 p. : $b ill., digital ; $c 24 cm.
490 1 $a Monografie matematyczne, $x 2297-0274 ; $v v. 67
505 0 $a Preface -- 1. Analytic Functions and Morse Theory -- 2. Normal Forms of Functions -- 3. Algebraic Topology of Manifolds -- 4. Topology and Monodromy of Functions -- 5. Integrals along Vanishing Cycles -- 6. Vector Fields and Abelian Integrals -- 7. Hodge Structures and Period Map -- 8. Linear Differential Systems -- 9. Holomorphic Foliations. Local Theory -- 10. Holomorphic Foliations. Global Aspects -- 11. The Galois Theory -- 12. Hypergeometric Functions -- Bibliography -- Index.
520 $a This book presents the monodromy group, underlining the unifying role it plays in a variety of theories and mathematical areas. In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. In the theory of systems of linear differential equations, one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations, there appear the Ecalle-Voronin-Martinet-Ramis moduli. Moreover, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. Readers will quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature. This second edition has been enlarged by several sections, presenting new results appeared since the first edition.
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650 1 4 $a Algebra. $3 516203
650 2 4 $a Algebraic Topology. $3 891269
650 2 4 $a Functions of a Complex Variable. $3 897310
650 2 4 $a Differential Equations. $3 907890
650 2 4 $a Special Functions. $3 897326
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830 0 $a Monografie matematyczne ; $v v. 67. $3 3784297
856 4 0 $u https://doi.org/10.1007/978-3-031-91270-2
950 $a Mathematics and Statistics (SpringerNature-11649)