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This volume presents the proceedings from the conference on"Topology, Geometry, and Algebra: Interactions and NewDirections" held in honor of R. James Milgram at StanfordUniversity in August 1999. The meeting brought togetherdistinguished researchers from a variety of areas related toalgebraic topology and its applications.

Papers in the book present a wide range of subjects, reflectingthe nature of the conference. Topics include moduli spaces,configuration spaces, surgery theory, homotopy theory, knottheory, group actions, and more. Particular emphasis was givento the breadth of interaction between the different areas. ... Read more

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The aim of this volume is to give an introduction and overview to differential topology, differential geometry and computational geometry with an emphasis on some interconnections between these three domains of mathematics. The chapters give the background required to begin research in these fields or at their interfaces. They introduce new research domains and both old and new conjectures in these different subjects show some interaction between other sciences close to mathematics. Topics discussed are; the basis of differential topology and combinatorial topology, the link between differential geometry and topology, Riemanian geometry (Levi-Civita connextion, curvature tensor, geodesic, completeness and curvature tensor), characteristic classes (to associate every fibre bundle with isomorphic fiber bundles), the link between differential geometry and the geometry of non smooth objects, computational geometry and concrete applications such as structural geology and graphism.

IOS Press is an international science, technical and medical publisher of high-quality books for academics, scientists, and professionals in all fields.

Some of the areas we publish in:

-Biomedicine
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This collection of papers honors the 100th anniversary of the birth of Boris Nikolaevich Delone, whose mathematical interests centered on the geometry of positive quadratic forms. After an initial paper presenting an account of Delone's life, including his scientific work, the book centers on discrete geometry and combinatorics. The book presents new methods that permit a description of the structure of some $L$-bodies and $L$-partitionings and that, in many cases, provide a definitive description. Also studied are combinatorial-topological problems arising in the statistical Ising model, the disposition of finite point sets in convex bodies of high dimension under certain conditions, and investigations of regular partitionings of spaces of constant curvature. ... Read more

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Papers from the conference. Provides a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st century mathematics. For graduate students and researchers in geometry and topology. ... Read more

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This volume contains the proceedings from the workshop on"Geometry, Topology and Dynamics" held at CRM at the Universityof Montreal. The event took place at a crucial time with respectto symplectic developments. During the previous year, Seibergand Witten had just introduced the famous gauge equations.Taubes then extracted new invariants that were shown to beequivalent in some sense to a particular form of Gromovinvariants for symplectic manifolds in dimension 4. WithGromov's deformation theory, this constitutes an importantadvance in symplectic geometry by furnishing existence criteria.

Meanwhile, contact geometry was rapidly developing. Using bothholomorphic arguments in symplectizations of contact manifoldsand ad hoc topological arguments---or even gauge theoreticmethods---several results were obtained on 3-dimensional contactmanifolds and new surprising facts were derived about theBennequin-Thurston invariant.

Furthermore, a fascinating relation exists between Hofer'sgeometry, pseudoholomorphic curves and the $K$-area recentlyintroduced by Gromov. Finally, longstanding conjectures on theflux were resolved in a substantial number of specific cases bycomparing various aspects of Floer-Novikov homology with Morsehomology.

The papers in this volume are written by leading experts and areall clear, comprehensive, and original. The work covers acomplete range of exciting new developments in symplectic andcontact geometries. ... Read more

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This volume consists of the written presentations of lectures given at two special sessions: the AMS Special Session on Topology in Dynamics (Winston-Salem, NC) and the AMS-AWM Special Session on Geometry in Dynamics (San Antonio, TX). Each article concerns aspects of the topology or geometry of dynamical systems. Topics covered include the following: foliations and laminations, iterated function systems, the three-body problem, isotopy stability, homoclinic tangles, fractal dimension, Morse homology, knotted orbits, inverse limits, contact structures, Grassmanians, blowups, and continua.

New results are presented reflecting current trends in topological aspects of dynamical systems. The book offers a wide variety of topics of special interest to those working this area bridging topology and dynamical systems. ... Read more

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This volume includes both survey and research articles on major advances and future developments in geometry and topology. Papers include those presented as part of the 5th Aarhus Conference---a meeting of international participants held in connection with ICM Berlin in 1998---and related papers on the subject.

This collection of papers is aptly published in the Contemporary Mathematics series, as the works represent the state of research and address areas of future development in the area of manifold theory and geometry. The survey articles in particular would serve well as supplemental resources in related graduate courses. ... Read more

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The workshop attracted more than 100 participants from various centres in Brazil, the US, Asia and Europe, ranging in experience from graduate students to leading experts in their field. The program covered topics in geometry, topology and physics, with special emphasis on harmonic maps, Kahler and contact geometry, gauge theory, low dimensional topology, and Seiberg-Witten theory. The contribution to this volume centre around a surprisingly deep interaction between quantum field theory from mathematical physics on the one hand and 4-dimensional topology on the other. Recent work by Witten and Seiberg makes this part of mathematics even more interesting and more powerful, which can be seen from articles in this volume. ... Read more

Customer Reviews (1)

Apanasov et al's Geometry, Topology, and Physics
The rapidly rising Brazilian, Mexican, and other Latin American schools in mathematics and physics are contributors to this remarkable volume published by Walter de Gruyter: Berlin.I will concentrate here on thearticle by J. Vaz, Jr., one of the world's greatest mathematicians andphysicists.In the following, I assume that the reader who is not aspecialist in this area will hire a reputable consultant or tutor totranslate the book into approximately ordinary English or elementarymath/physics, since the book gives valuable lessons for almost every fieldof interest.Vaz's paper is "Clifford algebra's and Witten's MonopoleEquations."See my reviews of Chisholm, Okubo, Benn, Baylis,Kursunoglu, and others on monopoles and Clifford algebras for some simpleexplanations.E. Witten is with the Institute for Advanced Study atPrinceton.It turns out that GUTs (Grand Unified Theories of theElementary Forces and Particles) predict the existence of monopoles, whichhave the remarkable property of being either north or south poles but notboth, unlike all magnets that we are familiar with in daily life.Diracand then t'Hooft have come up with basic monopole equations, and now Wittenhas also, and Vaz analyzes these using Clifford algebras. He reformulatesWitten's equations in Maxwell equation form using the idea of operatorspinors, and then obtains a representation without spinors and anotherrepresentation with an SU(2) connection related to the spinor connectionwith values in the Lie algebra of SU(2).An important theorem, theinversion theorem, is a major tool used by Vaz.The final reformulationinvolves the spinor covariant derivative acting on spinors.Lie algebrasare so remarkable that I will try to give some simple definitions for themin subsequent reviews of books on Lie algebras. ... Read more

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This collection contains articles reflecting the most recent activity in topology and mathematical physics presented at the S. Novikov Seminar held in Moscow. Papers in the volume are devoted to problems in geometry, topology, and mathematical physics, including applications of topology to physical problems. Such a combination is a long-standing tradition of the seminar, which originated in 1965. ... Read more

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This monograph deals with the geometrical and topologicalaspects associated with the quantization procedure, and it is shownhow these features are manifested in anomaly and Berry Phase. Thisbook is unique in its emphasis on the topological aspects of a fermionwhich arise as a consequence of the quantization procedure. Also, anoverview of quantization procedures is presented, tracing theequivalence of these methods by noting that the gauge field plays asignificant role in all these procedures, as it contains theingredients of topological features. Audience: This book will be of value to research workers andspecialists in mathematical physics, quantum mechanics, quantum fieldtheory, particle physics and differential geometry. ... Read more

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This textbook on geometry, topology and field theory covers a variety of areas, including modlui of anti-self-dual conformal structures, and problems on the structure of the mapping class group of surfaces and the topology of the moduli space of curves. ... Read more