By Marco Grandis

This is often the 1st authored ebook to be devoted to the hot box of directed algebraic topology that arose within the Nineteen Nineties, in homotopy concept and within the idea of concurrent strategies. Its normal target might be said as 'modelling non-reversible phenomena' and its area could be unusual from that of classical algebraic topology by means of the primary that directed areas have privileged instructions and directed paths therein needn't be reversible. Its homotopical instruments (corresponding within the classical case to boring homotopies, primary workforce and primary groupoid) may be equally 'non-reversible': directed homotopies, basic monoid and basic classification. Homotopy structures take place the following in a directed model, which provides upward push to new 'shapes', like directed cones and directed spheres. purposes will care for domain names the place privileged instructions seem, together with rewrite structures, site visitors networks and organic platforms. the main built examples are available within the sector of concurrency.

By Claudi Alsina, Roger Nelsen

Stable geometry is the normal identify for what we name at the present time the geometry of three-d Euclidean house. This ebook provides thoughts for proving quite a few geometric ends up in 3 dimensions. certain realization is given to prisms, pyramids, platonic solids, cones, cylinders and spheres, in addition to many new and classical effects. A bankruptcy is dedicated to every of the subsequent simple options for exploring area and proving theorems: enumeration, illustration, dissection, airplane sections, intersection, new release, movement, projection, and folding and unfolding. The ebook contains a choice of demanding situations for every bankruptcy with options, references and an entire index. The textual content is aimed toward secondary tuition and faculty and college lecturers as an advent to good geometry, as a complement in challenge fixing periods, as enrichment fabric in a direction on proofs and mathematical reasoning, or in a arithmetic direction for liberal arts scholars.

By Hajime Sato

The one so much tricky factor one faces whilst one starts to profit a brand new department of arithmetic is to get a think for the mathematical feel of the topic. the aim of this ebook is to aid the aspiring reader gather this crucial logic approximately algebraic topology in a quick time period. To this finish, Sato leads the reader via uncomplicated yet significant examples in concrete phrases. additionally, effects are usually not mentioned of their maximum attainable generality, yet when it comes to the easiest and so much crucial circumstances.

In reaction to feedback from readers of the unique variation of this booklet, Sato has additional an appendix of worthy definitions and effects on units, common topology, teams and such. He has additionally supplied references.

Topics coated comprise primary notions corresponding to homeomorphisms, homotopy equivalence, primary teams and better homotopy teams, homology and cohomology, fiber bundles, spectral sequences and attribute periods. items and examples thought of within the textual content contain the torus, the Möbius strip, the Klein bottle, closed surfaces, telephone complexes and vector bundles.

By A. J. Berrick, Man Chun Leung, Xingwang Xu

This e-book offers nineteen refereed articles written via individuals within the Singapore foreign Symposium in Topology and Geometry (SISTAG), held July 2-6, 2001, on the nationwide college of Singapore. instead of being an easy photo of the assembly within the type of a complaints, it serves as a commemorative quantity together with papers chosen to teach the range and intensity of the math offered at SISTAG. The e-book includes articles on low-dimensional topology, algebraic, differential and symplectic geometry, and algebraic topology. whereas papers replicate the focal point of the convention, many records written after SISTAG and incorporated during this quantity symbolize the newest pondering within the fields of topology and geometry.While illustration from Pacific Rim international locations is robust, the record of individuals is overseas in scope and comprises many well-known specialists. This quantity is of curiosity to graduate scholars and mathematicians operating within the fields of algebraic, differential and symplectic geometry, algebraic, geometric and low-dimensional topology, and mathematical physics

By R. Brown, T. L. Thickstun

This quantity comprises the lawsuits of a convention held on the collage collage of North Wales (Bangor) in July of 1979. It assembles study papers which replicate diversified currents in low-dimensional topology. The topology of 3-manifolds, hyperbolic geometry and knot concept come to be significant subject matters. The inclusion of surveys of labor in those components should still make the booklet very worthy to scholars in addition to researchers.

By Dominic D. Joyce

This graduate point textual content covers a thrilling and energetic quarter of study on the crossroads of numerous diverse fields in arithmetic and physics. In arithmetic it contains Differential Geometry, advanced Algebraic Geometry, Symplectic Geometry, and in physics String idea and reflect Symmetry. Drawing widely at the author's earlier paintings, the textual content explains the complicated arithmetic concerned easily and obviously to either mathematicians and physicists. beginning with the elemental geometry of connections, curvature, advanced and Kähler buildings appropriate for starting graduate scholars, the textual content covers seminal effects resembling Yau's facts of the Calabi Conjecture, and takes the reader the entire option to the frontiers of present study in calibrated geometry, giving many open difficulties.

By J Scott Carter

This article offers photographs that illustrates general examples in low dimensional topology. It starts off on the most simple point (the intersection of coordinate planes) and offers arms on structures of examples in topology: the projective aircraft, Poincare's instance of a homology sphere, lens areas, knotted surfaces, 2-sphere eversions and better dimensional manifolds. The textual content explains the significance of the examples and the recommendations with no being slowed down in technicalities. The booklet is a consultant to a large choice of subject matters. it may be of use to undergraduates who are looking to research geometric topology and to graduate scholars who wish examples with which they could make computations and who want an user-friendly description of topological areas. it may even be attention-grabbing to different scientists and mathematicians who are looking to research a few examples of topological areas.

By D. Repovs, P.V. Semenov

This ebook is devoted to the idea of continuing choices of multi­ valued mappings, a classical region of arithmetic (as some distance because the formula of its primary difficulties and strategies of options are involved) in addition to !'J-n sector which has been intensively constructing in fresh a long time and has came across a variety of functions usually topology, idea of absolute retracts and infinite-dimensional manifolds, geometric topology, fixed-point idea, sensible and convex research, online game concept, mathematical economics, and different branches of recent arithmetic. the basic leads to this the­ ory have been laid down within the mid 1950's through E. Michael. The booklet involves (relatively autonomous) 3 elements - half A: idea, half B: effects, and half C: purposes. (We shall discuss with those components just by their names). the objective viewers for the 1st half are scholars of arithmetic (in their senior 12 months or of their first 12 months of graduate college) who desire to get conversant in the rules of this idea. The target of the second one half is to offer a complete survey of the prevailing effects on non-stop decisions of multivalued mappings. it really is meant for experts during this sector in addition to should you have mastered the cloth of the 1st a part of the publication. within the 3rd half we current very important examples of functions of constant decisions. we've selected examples that are sufficiently fascinating and feature performed in a few feel key position within the corresponding components of arithmetic.

By Haynes R. Miller, Douglas C. Ravenel

Through the iciness and spring of 1985 a Workshop in Algebraic Topology used to be held on the college of Washington. The direction notes via Emmanuel Dror Farjoun and by means of Frederick R. Cohen contained during this quantity are rigorously written graduate point expositions of sure facets of equivariant homotopy thought and classical homotopy concept, respectively. M.E. Mahowald has incorporated a few of the fabric from his extra papers, signify quite a lot of modern homotopy idea: the Kervaire invariant, strong splitting theorems, computing device calculation of risky homotopy teams, and stories of L(n), Im J, and the symmetric teams.

By George M. Reed