Transcription of Spectral Sequences - Cornell University
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Spectral Sequences - Cornell University
Spectral SequencesAllen HatcherThis is a preliminary and incomplete version of an extra fifthchapter for myAl-gebraic Topologytextbook. Its aim is to give an introduction to Spectral Sequences asthey arise in algebraic topology. The rather lengthy first section of the chapter is de-voted to the Serre Spectral sequence and some of its main applications. After this, thesecond section gives a short introduction to the more specialized Adams Spectral se-quence, which is geared toward computing stable homotopy groups, especially stablehomotopy groups of spheres. The chapter then concludes withseveral independentsections on related topics and other Spectral Sequences . Here is a Table of Contentsfor the The Serre Spectral sequence .. 520 Exact Couples Serre Spectral sequence for Homology Classes and Further Properties Serre Spectral sequence for Cohomology Homotopy Groups of Spaces of Eilenberg-MacLane Spaces Homotopy Groups of Spheres The Adams Spectral sequence .
520 Chapter 5 Spectral Sequences One can think of a spectral sequence as a book consisting of a sequence of pages, each of which is a two-dimensional array of abelian groups. On each page there are maps between the groups, and these maps form chain complexes. The homology groups of these chain complexes are precisely the groups which appear on ...
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