On uniqueness of characteristic classes

Elisenda Feliu

doi:10.1016/j.jpaa.2010.08.006

On uniqueness of characteristic classes

Elisenda Feliu

Department of Mathematical Sciences

2 Citations (Scopus)

Abstract

We give an axiomatic characterization of maps from algebraic K-theory. The results apply to a large class of maps from algebraic K-theory to any suitable cohomology theory or to algebraic K-theory. In particular, we obtain comparison theorems for the Chern character and Chern classes and for the Adams operations and λ-operations on higher algebraic K-theory. We show that the Adams operations and λ-operations defined by Grayson agree with the ones defined by Gillet and Soulé.

Original language	English
Journal	Journal of Pure and Applied Algebra
Volume	215
Issue number	6
Pages (from-to)	1223-1242
Number of pages	20
ISSN	0022-4049
DOIs	https://doi.org/10.1016/j.jpaa.2010.08.006
Publication status	Published - Jun 2011

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http://www.sciencedirect.com/science/article/pii/S0022404910001775

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title = "On uniqueness of characteristic classes",

abstract = "We give an axiomatic characterization of maps from algebraic K-theory. The results apply to a large class of maps from algebraic K-theory to any suitable cohomology theory or to algebraic K-theory. In particular, we obtain comparison theorems for the Chern character and Chern classes and for the Adams operations and λ-operations on higher algebraic K-theory. We show that the Adams operations and λ-operations defined by Grayson agree with the ones defined by Gillet and Soul{\'e}.",

author = "Elisenda Feliu",

year = "2011",

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doi = "10.1016/j.jpaa.2010.08.006",

language = "English",

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N2 - We give an axiomatic characterization of maps from algebraic K-theory. The results apply to a large class of maps from algebraic K-theory to any suitable cohomology theory or to algebraic K-theory. In particular, we obtain comparison theorems for the Chern character and Chern classes and for the Adams operations and λ-operations on higher algebraic K-theory. We show that the Adams operations and λ-operations defined by Grayson agree with the ones defined by Gillet and Soulé.

AB - We give an axiomatic characterization of maps from algebraic K-theory. The results apply to a large class of maps from algebraic K-theory to any suitable cohomology theory or to algebraic K-theory. In particular, we obtain comparison theorems for the Chern character and Chern classes and for the Adams operations and λ-operations on higher algebraic K-theory. We show that the Adams operations and λ-operations defined by Grayson agree with the ones defined by Gillet and Soulé.

U2 - 10.1016/j.jpaa.2010.08.006

DO - 10.1016/j.jpaa.2010.08.006

M3 - Journal article

SN - 0022-4049

VL - 215

SP - 1223

EP - 1242

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 6

ER -

On uniqueness of characteristic classes

Abstract

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