Titlebook: Topological Methods in Group Theory; Ross Geoghegan Textbook 2008 Springer-Verlag New York 2008 Algebraic topology.CW complex.Cohomology.F

退出可食用

The Borel Construction and Bass-Serre Theoryis presented in Sect. 6.1; once it is in place, the Rebuilding Lemma 6.1.4 shows us how to alter ., without altering its homotopy type, to have more desirable properties. The important special case where . is a tree is discussed in §6.2. The reader may find it helpful to read Sects. 6.1 and 6.2 in p

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Homological Finiteness Properties of Groupsn Chapter 7. A free (or projective) resolution of the trivial .-module . plays the role of the universal cover of a . (., 1)-complex. The properties . and cohomological dimension are analogous to . and geometric dimension. This leads us to the Bestvina-Brady Theorem, which gives a method of construc

squander

COST

Cohomology of CW Complexeshere is an intriguing double duality in this. From one point of view ordinary cohomology is considered to be the “dual” of homology as defined in Chap. 2. From another point of view, which will be made precise when we discuss Poincaré Duality in Chap. 15, cohomology based on finite chains is “dual”

Freeze

Cohomology of Groups and Ends of Covering Spacesse involves the classical subject of ends of spaces and ends of groups. Our treatment of homology and cohomology of ends in Part III enables us to begin building a theory of “higher ends” of groups which will occupy much of the rest of the book.

heterogeneous

Mobile

Poincaré Duality in Manifolds and Groupsmension . — .. Ordinary homology is Poincaré dual to cohomology based on finite chains, and ordinary cohomology is Poincaré dual to homology based on infinite chains. The geometric treatment given here exhibits these duality isomorphisms at the level of chains in an intuitively satisfying way. Histo

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Textbook 2008t three kinds of readers in mind: graduate students who have had an introductory course in algebraic topology and who need a bridge from common knowledge to the current research literature in geometric, combinatorial and homological group theory; group theorists who would like to know more about the

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Cellular Homologyology: a formal way, given in terms of singular homology (Sects. 2.2, 2.3), and a geometrical way, in terms of incidence numbers and mapping degrees, given in Sect. 2.6 after an extensive discussion of degree and orientation in Sects. 2.4 and 2.5. The chapter ends with a presentation of the main points of homology in the cellular context.

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