The approximation theorem and the $K$-theory of generalized free products
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- by Roland Schwänzl and Ross E. Staffeldt PDF
- Trans. Amer. Math. Soc. 347 (1995), 3319-3345 Request permission
Abstract:
We use methods of abstract algebraic $K$-theory as developed by Friedhelm Waldhausen to give a new derivation of the decomposition theorem for the algebraic $K$-theory of a generalized free product ring. The result takes the form of a fibration sequence which relates the algebraic $K$-theory of such a ring with the algebraic $K$-theory of its factors, plus a Nil-term.References
- Randy McCarthy, On fundamental theorems of algebraic $K$-theory, Topology 32 (1993), no. 2, 325–328. MR 1217072, DOI 10.1016/0040-9383(93)90023-O
- J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358–426. MR 196736, DOI 10.1090/S0002-9904-1966-11484-2
- Daniel G. Quillen, Homotopical algebra, Lecture Notes in Mathematics, No. 43, Springer-Verlag, Berlin-New York, 1967. MR 0223432, DOI 10.1007/BFb0097438 Roland Schwänzl, Ross E. Staffeldt, and Friedhelm Waldhausen, Stable algebraic $K$-theory and topological Hochschild homology of ${A_\infty }$-rings, Preprint 94-003, SFB 343, Bielefeld. —, Decomposition theorems for $K$-theory of simplicial rings, in preparation.
- Ross E. Staffeldt, On fundamental theorems of algebraic $K$-theory, $K$-Theory 2 (1989), no. 4, 511–532. MR 990574, DOI 10.1007/BF00533280 Pierre Vogel, On the vanishing of Nil-groups, unpublished manuscript, 1990.
- Friedhelm Waldhausen, Algebraic $K$-theory of generalized free products. I, II, Ann. of Math. (2) 108 (1978), no. 1, 135–204. MR 498807, DOI 10.2307/1971165 —, Algebraic $K$-theory of spaces, Lecture Notes in Math., vol. 1126, Springer-Verlag, Berlin and New York, 1983, pp. 318-419.
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 3319-3345
- MSC: Primary 19D10; Secondary 19D35
- DOI: https://doi.org/10.1090/S0002-9947-1995-1303126-6
- MathSciNet review: 1303126