Titlebook: Rational Homotopy Theory and Differential Forms; Phillip Griffiths,John Morgan Book 2013Latest edition Springer Science+Business Media New

Instinctive

CW Homology Theorem,ogy of a CW complex can be computed from a chain complex whose chain groups have a generator for each cell and whose boundary map is determined from topological information about the attaching maps of the cells. The chapter finishes with some simple examples showing how to use the main result to mak

宿醉

thrombosis

Malleable

Postnikov Towers and Rational Homotopy Theory,on of localizing an abelian group at 0 is introduced, and the definition of a Q-space is given and then the existence and uniqueness of the localization of a space at 0 is established by localizing the Postnikov tower.

增減字母法

拱形面包

一再困擾

Homotopy Theory of DGAs,n is established. This obstruction theory is used to show that homotopy is an equivalence relation on maps from a given minimal DGA to another given DGA. From this, one establishes that any two minimal models for a given DGA are isomorphic by an isomorphism making the relevant diagram commute up to

上流社會

Ferritin

The Fundamental Group,rential forms. The notion of a 1-minimal model is introduced, and it is shown that every connected DGA has a 1-minimal model, unique up to isomorphism. The dual of this is a tower of nilpotent Lie algebras. We then turn to the nilpotent quotients of the fundamental group. The main result is that the

Munificent

Examples and Computations,mmetric spaces, and the classifying spaces BU(n) and BU. We also consider the graded Lie algebra defined by Whitehead products on homotopy groups. We consider the third homotopy group of a simply connected space and the homotopy theory of simply connected 4-manifolds. Lastly, we discuss products and