Exploring information geometry recent advances and connections to topological field theory Noémie C. Combe, Philippe G. Combe, Hanna K. Nencka

Format:

Book

Author/Creator:

Combe, Noémie C. (Noémie Cecile), 1990- author.

Combe, Philippe, 1940- author.

Nencka, Hanna, 1956- author.

Series:

Frontiers in mathematics

Baltic Institute of Mathematics collection

Frontiers in mathematics 1660-8054

Language:

English

Subjects (All):

Geometrical models in statistics.

Algebraic topology.

Physical Description:

1 online resource

Place of Publication:

Cham, Switzerland Birkhäuser [2026]

Summary:

"This book offers a clear and accessible pathway into information geometry for advanced undergraduate and graduate students. Readers will be guided from the fundamentals of topology and differentiable manifolds to the more advanced concepts of probability geometry and Frobenius manifolds in an intuitive manner, allowing them to build their knowledge gradually. Divided into three main parts, the first provides a concise introduction to differential topology and geometry, emphasizing the role of smooth manifolds, connections, and curvature in the formulation of geometric structures. Part II is then devoted to probability, measures, and statistics, where the notion of a probability space is refined into a geometric object, thus paving the way for a deeper mathematical understanding of statistical models. Finally, the third part introduces Frobenius manifolds, revealing their surprising connection to exponential families of probability distributions and, more broadly, their role in the geometry of information. Throughout all the chapters, there are exercises to test understanding, as well as solutions to some of the more challenging problems to aid learning"-- Springer Nature Link

Contents:

Foundations in general topology

Topological and modeled manifolds

Differentiability and Gateaux derivatives

Fiber bundles

Connections, parallel transport, and sheafs

Probability theory-measure theory-statistics

Categorical structures in probability and measure theory

Categorical and geometric structures in statistical manifold theory

Frobenius manifolds

Unveiling the hidden geometry of statistical manifolds

How Frobenius structures, paracomplex spaces meets Caph

Novel perspectives and openings

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Springer Nature Link, viewed July 29, 2026)

Other Format:

Print version Combe, Noémie C. (Noémie Cecile), 1990- Exploring information geometry

ISBN:

9783032230546

3032230543

OCLC:

1608208354

Access Restriction:

Restricted for use by site license