Category: Topology

Category: Topology

Category: Topology

Category: Topology

Category: Topology

Lectures on Surfaces (Student Mathematical Library, Volume by Anatole Katok, Vaughn Climenhaga

By Anatole Katok, Vaughn Climenhaga

Surfaces are one of the most typical and simply visualized mathematical gadgets, and their learn brings into concentration basic principles, thoughts, and techniques from geometry, topology, complicated research, Morse idea, and team idea. while, a lot of these notions look in a technically less complicated and extra picture shape than of their common ``natural'' settings. the 1st, essentially expository, bankruptcy introduces the various relevant actors--the around sphere, flat torus, Mobius strip, Klein bottle, elliptic aircraft, etc.--as good as a number of equipment of describing surfaces, starting with the conventional illustration through equations in 3-dimensional area, continuing to parametric illustration, and in addition introducing the fewer intuitive, yet valuable for our reasons, illustration as issue areas. It concludes with a initial dialogue of the metric geometry of surfaces, and the linked isometry teams. next chapters introduce basic mathematical structures--topological, combinatorial (piecewise linear), tender, Riemannian (metric), and complex--in the categorical context of surfaces. the focus of the booklet is the Euler attribute, which seems in lots of assorted guises and ties jointly strategies from combinatorics, algebraic topology, Morse concept, usual differential equations, and Riemannian geometry. The repeated visual appeal of the Euler attribute presents either a unifying subject and a strong representation of the proposal of an invariant in all these theories. The assumed historical past is the traditional calculus series, a few linear algebra, and rudiments of ODE and actual research. All notions are brought and mentioned, and nearly all effects proved, in line with this history. This e-book is as a result of the the MASS direction in geometry within the fall semester of 2007.

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Category: Topology

Cellular Structures in Topology by Rudolf Fritsch

By Rudolf Fritsch

This e-book describes the development and the houses of CW-complexes. those areas are very important simply because to start with they're the right kind framework for homotopy idea, and secondly such a lot areas that come up in natural arithmetic are of this sort. The authors speak about the rules and likewise advancements, for instance, the idea of finite CW-complexes, CW-complexes on the subject of the idea of fibrations, and Milnor's paintings on areas of the kind of CW-complexes. They determine very sincerely the connection among CW-complexes and the speculation of simplicial complexes, that's constructed in nice element. routines are supplied through the ebook; a few are straight forward, others expand the textual content in a non-trivial method. For the latter; extra reference is given for his or her answer. every one bankruptcy ends with a piece sketching the old improvement. An appendix supplies simple effects from topology, homology and homotopy conception. those beneficial properties will relief graduate scholars, who can use the paintings as a path textual content. As a modern reference paintings it will likely be crucial studying for the extra really expert staff in algebraic topology and homotopy idea.

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Category: Topology

Algebraic Methods in Unstable Homotopy Theory by Joseph Neisendorfer

By Joseph Neisendorfer

The main glossy and thorough remedy of volatile homotopy conception to be had. the point of interest is on these equipment from algebraic topology that are wanted within the presentation of effects, confirmed through Cohen, Moore, and the writer, at the exponents of homotopy teams. the writer introduces a number of facets of risky homotopy concept, together with: homotopy teams with coefficients; localization and of completion; the Hopf invariants of Hilton, James, and Toda; Samelson items; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems about the homotopy teams of spheres and Moore areas. This booklet is appropriate for a path in volatile homotopy conception, following a primary path in homotopy conception. it's also a worthy reference for either specialists and graduate scholars wishing to go into the sector.

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Category: Topology

Category: Topology

Euclidean Geometry in Mathematical Olympiads by Evan Chen

By Evan Chen

This is a not easy problem-solving e-book in Euclidean geometry, assuming not anything of the reader except a great deal of courage.

Topics coated integrated cyclic quadrilaterals, strength of some extent, homothety, triangle facilities; alongside the best way the reader will meet such classical gem stones because the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, in addition to the theorems of Euler, Ceva, Menelaus, and Pascal. one other half is devoted to using complicated numbers and barycentric coordinates, granting the reader either a standard and computational perspective of the fabric. the ultimate half contains a few extra complex themes, corresponding to inversion within the airplane, the go ratio and projective variations, and the speculation of the entire quadrilateral. The exposition is pleasant and secure, and followed by way of over three hundred superbly drawn figures.

The emphasis of this ebook is positioned squarely at the difficulties. each one bankruptcy comprises conscientiously selected labored examples, which clarify not just the ideas to the issues but in addition describe in shut element how one could invent the answer first of all. The textual content comprises as choice of three hundred perform difficulties of various trouble from contests worldwide, with large tricks and chosen solutions.

This e-book is principally appropriate for college students getting ready for nationwide or foreign mathematical olympiads, or for lecturers searching for a textual content for an honor class.

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Category: Topology

Combinatorial Methods in Topology and Algebra by Bruno Benedetti, Emanuele Delucchi, Luca Moci

By Bruno Benedetti, Emanuele Delucchi, Luca Moci

Combinatorics performs a renowned function in modern arithmetic, as a result of brilliant improvement it has skilled within the final twenty years and its many interactions with different subjects.

This publication arises from the INdAM convention "CoMeTA 2013 - Combinatorial equipment in Topology and Algebra,'' which was once held in Cortona in September 2013. the development introduced jointly rising and major researchers on the crossroads of Combinatorics, Topology and Algebra, with a specific specialize in new developments in matters comparable to: hyperplane preparations; discrete geometry and combinatorial topology; polytope concept and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial illustration theory.

The publication is split into elements. the 1st expands at the issues mentioned on the convention via offering extra heritage and factors, whereas the second one offers unique contributions on new traits within the themes addressed through the conference.

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