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This book consists of 16 surveys on Thurston's work and its later
development. The authors are mathematicians who were strongly
influenced by Thurston's publications and ideas. The subjects
discussed include, among others, knot theory, the topology of
3-manifolds, circle packings, complex projective structures,
hyperbolic geometry, Kleinian groups, foliations, mapping class
groups, Teichmuller theory, anti-de Sitter geometry, and
co-Minkowski geometry. The book is addressed to researchers and
students who want to learn about Thurston's wide-ranging
mathematical ideas and their impact. At the same time, it is a
tribute to Thurston, one of the greatest geometers of all time,
whose work extended over many fields in mathematics and who had a
unique way of perceiving forms and patterns, and of communicating
and writing mathematics.
This book consists of 16 surveys on Thurston's work and its later
development. The authors are mathematicians who were strongly
influenced by Thurston's publications and ideas. The subjects
discussed include, among others, knot theory, the topology of
3-manifolds, circle packings, complex projective structures,
hyperbolic geometry, Kleinian groups, foliations, mapping class
groups, Teichmuller theory, anti-de Sitter geometry, and
co-Minkowski geometry. The book is addressed to researchers and
students who want to learn about Thurston's wide-ranging
mathematical ideas and their impact. At the same time, it is a
tribute to Thurston, one of the greatest geometers of all time,
whose work extended over many fields in mathematics and who had a
unique way of perceiving forms and patterns, and of communicating
and writing mathematics.
This book explores the work of Bernhard Riemann and its impact on
mathematics, philosophy and physics. It features contributions from
a range of fields, historical expositions, and selected research
articles that were motivated by Riemann's ideas and demonstrate
their timelessness. The editors are convinced of the tremendous
value of going into Riemann's work in depth, investigating his
original ideas, integrating them into a broader perspective, and
establishing ties with modern science and philosophy. Accordingly,
the contributors to this volume are mathematicians, physicists,
philosophers and historians of science. The book offers a unique
resource for students and researchers in the fields of mathematics,
physics and philosophy, historians of science, and more generally
to a wide range of readers interested in the history of ideas.
This is a two-volume collection presenting the selected works of
Herbert Busemann, one of the leading geometers of the twentieth
century and one of the main founders of metric geometry, convexity
theory and convexity in metric spaces. Busemann also did
substantial work (probably the most important) on Hilbert's Problem
IV. These collected works include Busemann's most important
published articles on these topics. Volume I of the collection
features Busemann's papers on the foundations of geodesic spaces
and on the metric geometry of Finsler spaces. Volume II includes
Busemann's papers on convexity and integral geometry, on Hilbert's
Problem IV, and other papers on miscellaneous subjects. Each volume
offers biographical documents and introductory essays on Busemann's
work, documents from his correspondence and introductory essays
written by leading specialists on Busemann's work. They are a
valuable resource for researchers in synthetic and metric geometry,
convexity theory and the foundations of geometry.
This book explores the work of Bernhard Riemann and its impact on
mathematics, philosophy and physics. It features contributions from
a range of fields, historical expositions, and selected research
articles that were motivated by Riemann's ideas and demonstrate
their timelessness. The editors are convinced of the tremendous
value of going into Riemann's work in depth, investigating his
original ideas, integrating them into a broader perspective, and
establishing ties with modern science and philosophy. Accordingly,
the contributors to this volume are mathematicians, physicists,
philosophers and historians of science. The book offers a unique
resource for students and researchers in the fields of mathematics,
physics and philosophy, historians of science, and more generally
to a wide range of readers interested in the history of ideas.
Despite its importance in the history of Ancient science, Menelaus'
Spherics is still by and large unknown. This treatise, which lies
at the foundation of spherical geometry, is lost in Greek but has
been preserved in its Arabic versions. The reader will find here,
for the first time edited and translated into English, the
essentials of this tradition, namely: a fragment of an early Arabic
translation and the first Arabic redaction of the Spherics composed
by al-Mahani /al-Harawi, together with a historical and
mathematical study of Menelaus' treatise. With this book, a new and
important part of the Greek and Arabic legacy to the history of
mathematics comes to light. This book will be an indispensable
acquisition for any reader interested in the history of Ancient
geometry and science and, more generally, in Greek and Arabic
science and culture.
Gromov's theory of hyperbolic groups have had a big impact in
combinatorial group theory and has deep connections with many
branches of mathematics suchdifferential geometry, representation
theory, ergodic theory and dynamical systems. This book is an
elaboration on some ideas of Gromov on hyperbolic spaces and
hyperbolic groups in relation with symbolic dynamics. Particular
attention is paid to the dynamical system defined by the action of
a hyperbolic group on its boundary. The boundary is most
oftenchaotic both as a topological space and as a dynamical system,
and a description of this boundary and the action is given in terms
of subshifts of finite type. The book is self-contained and
includes two introductory chapters, one on Gromov's hyperbolic
geometry and the other one on symbolic dynamics. It is intended for
students and researchers in geometry and in dynamical systems, and
can be used asthe basis for a graduate course on these subjects.
The purpose of this volume and of the other volumes in the same
series is to provide a collection of surveys that allows the reader
to learn the important aspects of William Thurston’s heritage.
Thurston’s ideas have altered the course of twentieth century
mathematics, and they continue to have a significant influence on
succeeding generations of mathematicians. The topics covered in the
present volume include com-plex hyperbolic Kleinian groups, Möbius
structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm,
surgeries in representation varieties, triangulations, spaces of
polygo-nal decompositions and of singular flat structures on
surfaces, combination theorems in the theories of Kleinian groups,
hyperbolic groups and holomorphic dynamics, the dynamics and
iteration of rational maps, automatic groups, and the combinatorics
of right-angled Artin groups.
This volume presents the beautiful memoirs of Euler, Lagrange and
Lambert on geography, translated into English and put into
perspective through explanatory and historical essays as well as
commentaries and mathematical notes. These works had a major impact
on the development of the differential geometry of surfaces and
they deserve to be studied, not only as historical documents, but
most of all as a rich source of ideas.
The purpose of this volume and of the other volumes in the same
series is to provide a collection of surveys that allows the reader
to learn the important aspects of William Thurston's heritage.
Thurston's ideas have altered the course of twentieth century
mathematics, and they continue to have a significant influence on
succeeding generations of mathematicians. The topics covered in the
present volume include com-plex hyperbolic Kleinian groups, Moebius
structures, hyperbolic ends, cone 3-manifolds, Thurston's norm,
surgeries in representation varieties, triangulations, spaces of
polygo-nal decompositions and of singular flat structures on
surfaces, combination theorems in the theories of Kleinian groups,
hyperbolic groups and holomorphic dynamics, the dynamics and
iteration of rational maps, automatic groups, and the combinatorics
of right-angled Artin groups.
The volume consists of a set of surveys on geometry in the broad
sense. The goal is to present a certain number of research topics
in a non-technical and appealing manner. The topics surveyed
include spherical geometry, the geometry of finite-dimensional
normed spaces, metric geometry (Bishop-Gromov type inequalities in
Gromov-hyperbolic spaces), convexity theory and inequalities
involving volumes and mixed volumes of convex bodies, 4-dimensional
topology, Teichmuller spaces and mapping class groups actions,
translation surfaces and their dynamics, and complex
higher-dimensional geometry. Several chapters are based on lectures
given by their authors to middle-advanced level students and young
researchers. The whole book is intended to be an introduction to
current research trends in geometry.
Groups and group actions are probably the most central objects in
mathematics. Comprising volumes 31, 32, 40 and 41 of the ALM
series, the Handbook of Group Actions presents survey articles on
the topic of group actions and how they appear in several
mathematical contexts. The general subject matter is organized
under the following sections: geometry, mapping class groups, knot
groups, topology, representation theory, deformation theory, and
discrete groups. The various articles deal with both classical
material and modern developments. They are written by specialists
in their respective subject areas, and addressed to graduate
students who want to learn the theory, as well as to specialists as
a reference. This is the fourth volume of the Handbook of Group
Actions.
This is a collection of surveys on important mathematical ideas,
their origin, their evolution and their impact in current research.
The authors are mathematicians who are leading experts in their
fields. The book is addressed to all mathematicians, from
undergraduate students to senior researchers, regardless of the
specialty.
This is a collection of surveys on important mathematical ideas,
their origin, their evolution and their impact in current research.
The authors are mathematicians who are leading experts in their
fields. The book is addressed to all mathematicians, from
undergraduate students to senior researchers, regardless of the
specialty.
Groups and group actions are probably the most central objects in
mathematics. Comprising volumes 31, 32, 40 and 41 of the ALM
series, the Handbook of Group Actions presents survey articles on
the topic of group actions and how they appear in several
mathematical contexts. The general subject matter is organized
under the following sections: geometry, mapping class groups, knot
groups, topology, representation theory, deformation theory, and
discrete groups. The various articles deal with both classical
material and modern developments. They are written by specialists
in their respective subject areas, and addressed to graduate
students who want to learn the theory, as well as to specialists as
a reference. This is the third volume of the Handbook of Group
Actions.
Groups and group actions are probably the most central objects in
mathematics. Comprising volumes 31, 32, 40 and 41 of the ALM
series, the Handbook of Group Actions presents survey articles on
the topic of group actions and how they appear in several
mathematical contexts. The general subject matter is organized
under the following sections: geometry, mapping class groups, knot
groups, topology, representation theory, deformation theory, and
discrete groups. The various articles deal with both classical
material and modern developments. They are written by specialists
in their respective subject areas, and addressed to graduate
students who want to learn the theory, as well as to specialists as
a reference. This is the four-volume set.
Groups and group actions are probably the most central objects in
mathematics. Comprising volumes 31 and 32 of the ALM series (with
further volumes forthcoming), the Handbook of Group Actions
presents survey articles on the topic of group actions and how they
appear in several mathematical contexts. The general subject matter
is organized under the following sections: geometry, mapping class
groups, knot groups, topology, representation theory, deformation
theory, and discrete groups. The various articles deal with both
classical material and modern developments. They are written by
specialists in their respective subject areas, and addressed to
graduate students who want to learn the theory, as well as to
specialists as a reference. This is the first volume of the
Handbook of Group Actions.
Groups and group actions are probably the most central objects in
mathematics. Comprising volumes 31 and 32 of the ALM series (with
further volumes forthcoming), the Handbook of Group Actions
presents survey articles on the topic of group actions and how they
appear in several mathematical contexts. The general subject matter
is organized under the following sections: geometry, mapping class
groups, knot groups, topology, representation theory, deformation
theory, and discrete groups. The various articles deal with both
classical material and modern developments. They are written by
specialists in their respective subject areas, and addressed to
graduate students who want to learn the theory, as well as to
specialists as a reference. This is the second volume of the .
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