×
Grayson, Daniel R.

Adams operations on higher \(K\)-theory. (English) Zbl 0776.19001

\(K\)-Theory 6, No. 2, 97-111 (1992).
Let \(\mathcal P\) be an exact category with suitable notions of tensor product, symmetric product and exterior product. The author constructs combinatorial maps inducing the Adams operations in the higher algebraic \(K\)-theory of \(\mathcal P\). These maps are one-fold deloopings of the maps which can be constructed by using lambda operations.
Reviewer: R.J.Steiner (Glasgow)

Cited in 2 Reviews
Cited in 16 Documents

MSC:

19D23 Symmetric monoidal categories
19L10 Riemann-Roch theorems, Chern characters

Keywords:

Adams operations; higher algebraic \(K\)-theory; one-fold deloopings

Citations:

Zbl 0701.18007
PDF BibTeX XML Cite
\textit{D. R. Grayson}, \(K\)-Theory 6, No. 2, 97--111 (1992; Zbl 0776.19001)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Bass, H.:Algebraic K-theory, W. A. Benjamin, New York.
[2] Dold and Puppe:Ann. Inst Fourier 11 (1961), 201–312.
[3] Gillet, H. and Grayson, D.: On the loop space of theQ-construction,Illinois J. Math. 31 (1987), 574–597. · Zbl 0628.55011
[4] Gillet, H. and Soulé, C.:K-théorie et nullité des multiplicités d’intersection,C. R. Acad. Sci. Pairs 300 (1985), 71–74. · Zbl 0587.13007
[5] Grayson, D.: Exterior power operations on algebraicK-theory,K-Theory 3 (1989), 247–260. · Zbl 0701.18007
[6] Grothendieck, A.:Revêtements étales et groupe fondamental, Séminaire de Géométrie Algébrique du Bois-Marie 1960/61,SGA 1, Lecture Notes in Math. 224, Springer, New York, 1971.
[7] Grothendieck, A.: La théorie des classes de Chern,Bull. Soc. Math. France 86 (1958), 137–154. · Zbl 0091.33201
[8] Hiller, H. L.: {\(\lambda\)}-rings and algebraicK-theory,J. Pure Appl. Algebra 20 (1981), 241–266. · Zbl 0471.18007
[9] Kratzer, Ch.: {\(\lambda\)}-Structure enK-théorie algébrique,Comment. Math. Helv. 55 (1980), 233–254. · Zbl 0444.18008
[10] Lecomte, F.: Opérations d’Adams enK-Théorie algébrique, part of her thesis.
[11] Nenashev, A.: in preparation.
[12] Paluch, M.: Thesis at University of Illinois at Chicago (1991).
[13] Schechtmann, V.:K-Theory, Arithmetic, and Geometry, Lecture Notes in Math. 1289, Springer, New York, 1987.
[14] Waldhausen, F.: AlgebraicK-theory of generalized free products,Ann. of Math. 108 (1978), 135–256. · Zbl 0397.18012
[15] Waldhausen, F.:Algebraic and Geometric Topology (Rutgers 1983), Lecture Notes in Math. 1126, Springer, New York, 1985.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.