Polynomials and Vanishing Cycles by Mihai Tibr
The behaviour of vanishing cycles is the cornerstone for understanding the geometry and topology of families of hypersurfaces, usually regarded as singular fibrations. This self-contained tract proposes a systematic geometro-topological approach to vanishing cycles, especially those appearing in non-proper fibrations, such as the fibration defined by a polynomial function. Topics which have been the object of active research over the past 15 years, such as holomorphic germs, polynomial functions, and Lefschetz pencils on quasi-projective spaces, are here shown in a new light: conceived as aspects of a single theory with vanishing cycles at its core. Throughout the book the author presents the current state of the art. Transparent proofs are provided so that non-specialists can use this book as an introduction, but all researchers and graduate students working in differential and algebraic topology, algebraic geometry, and singularity theory will find this book of great use.-
The Geometry of Fractal Sets
-
Riemannian Geometry
-
Miniquaternion Geometry
-
The Geometry of Total Curvature on Complete Open Surfaces
-
Metric Spaces
-
Birational Geometry and Manin's Conjecture
-
Coherence in Three-Dimensional Category Theory
-
Dilation and Model Theory for Pairs of Commuting Contraction Operators
-
The Direct Method in Soliton Theory
-
Matrix Positivity
-
Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem
-
Topics in Critical Point Theory
-
Category and Measure
-
The Mathieu Groups
-
Modern Approaches to the Invariant-Subspace Problem
-
Frobenius Manifolds and Moduli Spaces for Singularities
-
Group Cohomology and Algebraic Cycles
-
Permutation Group Algorithms
-
Nonlinear Perron–Frobenius Theory
-
Abelian Varieties, Theta Functions and the Fourier Transform
-
Matrices of Sign-Solvable Linear Systems
-
The Cube-A Window to Convex and Discrete Geometry
-
The Large Sieve and its Applications
-
Combinatorics of Minuscule Representations
-
Restricted Orbit Equivalence for Actions of Discrete Amenable Groups
-
Metric Diophantine Approximation on Manifolds
-
Applications of Diophantine Approximation to Integral Points and Transcendence
-
An Introduction to Homotopy Theory
-
Linear and Projective Representations of Symmetric Groups
-
Dependence with Complete Connections and its Applications
-
Fixed Point Theory and Applications
-
Justification Logic
-
Synthetic Geometry of Manifolds
-
Dynamical Systems and Semisimple Groups
-
Distribution Modulo One and Diophantine Approximation
-
The Levy Laplacian
-
Sets of Multiples
-
Period Domains over Finite and p-adic Fields
-
Large Deviations for Markov Chains
-
Levy Processes in Lie Groups
-
Character Sums with Exponential Functions and their Applications
-
Poincare Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations
-
Quasi-Frobenius Rings
-
The Covering Property Axiom, CPA
-
Ridge Functions
-
Jordan Structures in Geometry and Analysis
-
Typical Dynamics of Volume Preserving Homeomorphisms
'… written in a clear didactic style, with detailed explanations of all notions and results … the book reads fluently, it is accessible for graduate students while advanced researchers … can find here very interesting and useful material …' Zentralblatt MATH
'Each chapter of the book is followed by exercises …' EMS Newsletter
'Each chapter of the book is followed by exercises …' EMS Newsletter
Mihair Tibar is a Professor in the Mathematics Department at the Université des Sciences et Technologies de Lille, France.
| SKU | Unavailable |
| ISBN 13 | 9780521829205 |
| ISBN 10 | 0521829208 |
| Title | Polynomials and Vanishing Cycles |
| Author | Mihai Tibr |
| Series | Cambridge Tracts In Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2007-05-17 |
| Number of pages | 266 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |