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A First Course in Abstract Algebra by Hiram Paley

By Hiram Paley

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In: Geometry and Topology: Aarhus (1998). Contemporary Mathematics, vol. 258, pp. 351–368. American Mathematical Society, Providence (2000) 38. : K -theory homology of spaces. In: Algebraic Topology (Arcata. CA, 1986), pp. 346–361. Springer, Berlin (1989) 39. : Ends of maps. I. Ann. Math. (2), 110(2), 275–331 (1979) 40. : Algebraic K -theory over virtually abelian groups. J. Pure Appl. Algebra 216(1), 170–183 (2012) 41. : Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K -theory (2011).

2 The Farrell-Jones Conjecture and Its Fibered Version In this work we are interested in the formulations of the Farrell-Jones Isomorphism Conjecture, in both, its fibered and nonfibered versions. Let K be the Davis-Lück algebraic K theory functor, see [8, Sect. 2] and let L be the Davis-Lück L −∞ theory functor, see [8, Sect. 2] and [9, Sect. 3] for the definition of L −∞ -theory (or L theory for short). The validity of this conjecture allows us, in principle, to compute the algebraic K or L theory groups of the group ring of a given group G from (a) the corresponding K or L theory groups of the group rings of virtually cyclic subgroups of G and (b) homological information.

1 Constructing the Whitehead manifold T0 T1 3 No expertise in cosmology is being claimed by the author.

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