By Edwin Hewitt, Kenneth A. Ross

This ebook is a continuation of vol. I (Grundlehren vol. one hundred fifteen, additionally to be had in softcover), and encompasses a particular therapy of a few very important elements of harmonic research on compact and in the community compact abelian teams. From the stories: "This paintings goals at giving a monographic presentation of summary harmonic research, way more entire and entire than any publication already present at the subject...in reference to each challenge taken care of the publication deals a many-sided outlook and leads as much as most up-to-date advancements. Carefull cognizance can be given to the historical past of the topic, and there's an intensive bibliography...the reviewer believes that for a few years to come back it will stay the classical presentation of summary harmonic analysis." Publicationes Mathematicae

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30see Burger–Monod, Geom. Funct. , 12(2):219–280, 2002. n = 2: Burger–Monod, in Rigidity in dynamics and geometry, 19–37, Springer 2002. For n ≥ 3: N. Monod, Contemp. Math. 347:191–202, AMS 2004. 32Q. J. , 53(1):59–73, 2002. 31For 40 GUIDO’S BOOK OF CONJECTURES 17. Cornelia M. Busch Worry about primes in Farrell cohomology Dear Guido, we suffered headache while I was thinking about the following question. 1. Let p be any odd prime, and let Sp(p − 1, Z[1/n]) denote the group of symplectic (p − 1) × (p − 1)-matrices over Z[1/n], where 0 = n ∈ Z is any nonzero integer.

The localization of any 1-connected space is 1-connected. A weaker version: A universal covering projection X → X is a localization map only if is it an equivalence, namely, X is 1-connected. Problem 6. Any localization of a polyGEM is a polyGEM. The localization of an n-connected Postnikov stage is an n-connected Postnikov stage. Problem 7. A version of problem 3. Suppose X = cellA M where M is an f -local space, for some f,— say a K(π, 1). Then X ∼ = cellA Lf X. This is true in several special cases, say for finitely generated abelian groups.

4) Moreover, a counterexample of the first type implies the existence of a counterexample of the second type (6). Our concern here is with the finite case of the conjecture, namely the assertion that any subcomplex of a finite aspherical 2-complex is also aspherical. This assertion implies that (a) above does not hold. An interesting question is whether the negation of (a) above is actually equivalent to the finite case of the conjecture. If X is a finite 2-complex such that Y = X ∪f e2 is contractible then π = π1 (X) has a presentation of deficiency 1 (since χ(X) = 0), and π is the normal closure of the element represented by the attaching map f ; so π has weight 1.