By K Heiner Kamps, Timothy Porter

Summary homotopy concept relies at the statement that analogues of a lot of topological homotopy idea and easy homotopy idea exist in lots of different different types, akin to areas over a set base, groupoids, chain complexes and module different types. learning express models of homotopy constitution, equivalent to cylinders and course area buildings allows not just a unified improvement of many examples of identified homotopy theories, but additionally finds the interior operating of the classical spatial idea, truly indicating the logical interdependence of homes (in specific the lifestyles of yes Kan fillers in linked cubical units) and effects (Puppe sequences, Vogt's lemma, Dold's Theorem on fibre homotopy equivalences, and homotopy coherence idea)

By Yu. I. Manin, Alexei A. Panchishkin

This variation has been known as ‘startlingly up-to-date’, and during this corrected moment printing you'll be convinced that it’s much more contemporaneous. It surveys from a unified viewpoint either the fashionable country and the developments of continuous improvement in numerous branches of quantity idea. Illuminated through undemanding difficulties, the valuable principles of contemporary theories are laid naked. a few themes lined contain non-Abelian generalizations of sophistication box conception, recursive computability and Diophantine equations, zeta- and L-functions. This considerably revised and multiplied re-creation comprises numerous new sections, similar to Wiles' evidence of Fermat's final Theorem, and appropriate concepts coming from a synthesis of varied theories.

By R.K. Lazarsfeld

Quantity paintings containing a latest account on "Positivity in Algebraic Geometry".

Both volumes additionally to be had as hardcover variants as Vols. forty eight and forty nine within the sequence "Ergebnisse der Mathematik und ihrer Grenzgebiete".

A good buy of the fabric has now not formerly seemed in e-book form.

Volume II is extra on the examine level and slightly extra really expert than quantity I.

Volume II encompasses a survey of positivity for vector bundles, and strikes directly to a scientific improvement of the speculation of multiplier beliefs and their applications. 

Contains many concrete examples, functions, and tips that could additional developments

By Klaus Lamotke (auth.)

Das vorliegende Buch beruht auf Vorlesungen und Seminaren fur Studenten mittlerer und hoherer Semester im Anschlu? an eine Einfuhrung in die komplexe Funktionentheorie. Die Theorie Riemannscher Flachen wird als ein Mikrokosmos der Reinen Mathematik dargestellt, in dem Methoden der Topologie und Geometrie, der komplexen und reellen research sowie der Algebra zusammenwirken, um die reichhaltige Struktur dieser Flachen aufzuklaren und an vielen Beispielen und Bildern zu erlautern, die in der historischen Entwicklung eine Rolle spielten. Wegen seiner Methodenvielfalt enthalt das Buch gleichzeitig Einfuhrungen in die Topologie (Fundamentalgruppe, Uberlagerungen, Flachen), in die algebraische Geometrie (Kurven und ihre Singularitaten) und in die Potentialtheorie (Perron-Prinzip).

By Masoud Khalkhali

This is often the 1st present quantity that collects lectures in this very important and quick constructing topic in arithmetic. The lectures are given by means of prime specialists within the box and the diversity of themes is stored as huge as attainable through together with either the algebraic and the differential points of noncommutative geometry in addition to fresh functions to theoretical physics and quantity thought.

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