The Homotopy Category Of Simply Connected 4-manifolds (london Mathematical Society Lecture Note Series)

The Homotopy Type Of A Closed Simply Connected 4-manifold Is Determined By The Intersection Form. The Homotopy Classes Of Maps Between Two Such Manifolds, However, Do Not Coincide With The Algebraic Morphisms Between Intersection Forms. Therefore The Problem Arises Of Computing The Homotopy Classes Of Maps Algebraically And Determining The Law Of Composition For Such Maps. This Problem Is Solved In The Book By Introducing New Algebraic Models Of A 4-manifold. The Book Has Been Written To Appeal To Both Established Researchers In The Field And Graduate Students Interested In Topology And Algebra. There Are Many References To The Literature For Those Interested In Further Reading. 1. Homotopy Category Of (2,4)-complexes -- 2. Homotopy Category Of Simply Connected 4-manifolds -- 3. Track Categories -- 4. Splitting Of The Linear Extension Tl -- 5. Category T[gamma] And An Algebraic Model Of Cw(2,4) -- 6. Crossed Chain Complexes And Algebraic Models Of Tracks -- 7. Quadratic Chain Complexes And Algebraic Models Of Tracks -- 8. On The Cohomology Of The Category Nil. (t. Pirashvili). Hans Joachim Baues. Includes Bibliographical References (p. [179]-181) And Index. This study is concerned with computing the homotopy classes of maps algebraically and determining the law of composition for such maps. The problem is solved by introducing new algebraic models of a 4-manifold. Including a complete list of references for the text, the book appeals to researchers and graduate students in topology and algebra. A book on homotopy theory, written to appeal to both established researchers in the field and graduate students interested in topology and algebra. The techniques used in this book include the use of some new algebraic models of 4-manifolds. There is a full list of references.