Download E-books Abstract Homotopy and Simple Homotopy Theory PDF

By Klaus Heiner Kamps

Summary homotopy idea relies at the statement that analogues of a lot of topological homotopy thought and easy homotopy concept exist in lots of different different types, similar to areas over a hard and fast base, groupoids, chain complexes and module different types. learning express types of homotopy constitution, akin to cylinders and direction area structures permits not just a unified improvement of many examples of recognized homotopy theories, but in addition unearths the internal operating of the classical spatial idea, in actual fact indicating the logical interdependence of homes (in specific the life of sure Kan fillers in linked cubical units) and effects (Puppe sequences, Vogt's lemma, Dold's Theorem on fibre homotopy equivalences, and homotopy coherence theory).

Show description

Read Online or Download Abstract Homotopy and Simple Homotopy Theory PDF

Similar Algebraic Geometry books

Analytic K-Homology (Oxford Mathematical Monographs)

This paintings attracts jointly rules from algebraic topology, useful research and geometry. it's a device - a method of conveying info between those 3 topics - and it's been used with good fortune to find theorems throughout a large span of arithmetic. the aim of this publication is to acquaint the reader with the fundamental principles of analytic K-homology and advance a few of its functions.

The Geometry of Topological Stability (London Mathematical Society Monographs)

In providing an in depth learn of the geometry and topology of various periods of "generic" singularities, Geometry of Topological balance bridges the space among algebraic calculations and continuity arguments to aspect the mandatory and enough stipulations for a C (infinity) to be C]0-stable. all through, the authors masterfully learn this significant topic utilizing effects culled from a wide variety of mathematical disciplines, together with geometric topology, stratification idea, algebraic geometry, and commutative algebra.

Lectures on Polytopes (Graduate Texts in Mathematics)

According to a graduate direction on the Technische Universit├Ąt, Berlin, those lectures current a wealth of fabric at the smooth thought of convex polytopes. the simple exposition gains many illustrations, and whole proofs for many theorems. With basically linear algebra as a prerequisite, it takes the reader fast from the fundamentals to issues of modern examine.

Higher-Dimensional Algebraic Geometry (Universitext)

The class concept of algebraic forms is the point of interest of this booklet. This very energetic zone of study remains to be constructing, yet an grand volume of information has gathered during the last 20 years. The authors objective is to supply an simply obtainable advent to the topic. The ebook starts off with preparatory and conventional definitions and effects, then strikes directly to talk about quite a few points of the geometry of gentle projective types with many rational curves, and finishes in taking the 1st steps in the direction of Moris minimum version application of category of algebraic forms through proving the cone and contraction theorems.

Extra resources for Abstract Homotopy and Simple Homotopy Theory

Show sample text content

Rated 4.97 of 5 – based on 29 votes