Abstract
In this paper we describe the boundary map ε: K3(A/J) → K2(A,J) in the algebraic K-theory exact sequence *
where K3 is given in terms of Igusa’s “pictures” [2,3,4] and K2(A,J) has the presentation given independently by Keune [5] and Loday [6]. One use of this explicit description of ε is in computing some examples of the K3 invariant for π1 DIff (M).
Partially supported by NSF MCS 7704242.
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References
A.Hatcher and J.Wagoner, Pseudo-isotopies of compact manifolds, Astérisque No. 6, Société Mathématique de France.
K.Igusa, The Wh3(π) obstruction for pseudo-isotopy, Thesis, Princeton University, 1978, to appear in Springer-Verlag Lecture Notes in Mathematics.
—, The generalized Grassman invariant K3(Z[π]) → H0(π;Z2[π]), preprint Brandeis University, to appear in Springer-Verlag Lecture Notes in Mathematics.
—, to appear in "Pseudo-isotopy," forthcoming volume in Springer-Verlag Lecture Notes in Mathematics.
F. Keune, The relativization of K2, Jour. of Alg., Vol. 54, No. 1, 1978, pp. 159–177.
J.-L. Loday, Cohomologie et groupe de Steinberg relatifs, Jour. of Alg., Vol. 54, No. 1, 1978, pp. 178–202.
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© 1982 Springer-Verlag
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Wagoner, J.B. (1982). A picture description of the boundary map in algebraic K-theory. In: Dennis, R.K. (eds) Algebraic K-Theory. Lecture Notes in Mathematics, vol 966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062184
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DOI: https://doi.org/10.1007/BFb0062184
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