### Abstract

The natural transformation Xi from L-theory to the Tate cohomology of Z/2 acting on K-theory commutes with external products. Corollary: The Tate cohomology of Z/2 actingon the K-theory of any ring with involution is a generalized Eilenberg-Mac Lane spectrum, and it is 4-periodic.

Original language | English |
---|---|

Pages (from-to) | 689-709 |

Number of pages | 21 |

Journal | Transactions of the American Mathematical Society |

Volume | 352 |

Publication status | Published - 2000 |

### Keywords

- products
- ring spectrum
- Tate cohomology
- surgery
- ALGEBRAIC K-THEORY
- SPACES
- SEGAL
- FORMS

### Cite this

*Transactions of the American Mathematical Society*,

*352*, 689-709.

**Products and duality in Waldhausen categories.** / Weiss, M S ; Williams, B .

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 352, pp. 689-709.

}

TY - JOUR

T1 - Products and duality in Waldhausen categories

AU - Weiss, M S

AU - Williams, B

PY - 2000

Y1 - 2000

N2 - The natural transformation Xi from L-theory to the Tate cohomology of Z/2 acting on K-theory commutes with external products. Corollary: The Tate cohomology of Z/2 actingon the K-theory of any ring with involution is a generalized Eilenberg-Mac Lane spectrum, and it is 4-periodic.

AB - The natural transformation Xi from L-theory to the Tate cohomology of Z/2 acting on K-theory commutes with external products. Corollary: The Tate cohomology of Z/2 actingon the K-theory of any ring with involution is a generalized Eilenberg-Mac Lane spectrum, and it is 4-periodic.

KW - products

KW - ring spectrum

KW - Tate cohomology

KW - surgery

KW - ALGEBRAIC K-THEORY

KW - SPACES

KW - SEGAL

KW - FORMS

M3 - Article

VL - 352

SP - 689

EP - 709

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

ER -