On the algebraic $L$-theory of $\Delta$-sets

Andrew Ranicki; Michael Weiss

On the algebraic $L$-theory of $\Delta$-sets

Algebraic Topology 2010-09-27 v2 Geometric Topology

Authors: Andrew Ranicki , Michael Weiss

Abstract

The algebraic $L$ -groups $L_*(\A,X)$ are defined for an additive category $\A$ with chain duality and a $\Delta$ -set $X$ , and identified with the generalized homology groups $H_*(X;\LL_{\bullet}(\A))$ of $X$ with coefficients in the algebraic $L$ -spectrum $\LL_{\bullet}(\A)$ . Previously such groups had only been defined for simplicial complexes $X$ .

Keywords

lie algebra abelian groups algebra classification and gradings

Cite

@article{arxiv.math/0701833,
  title  = {On the algebraic $L$-theory of $\Delta$-sets},
  author = {Andrew Ranicki and Michael Weiss},
  journal= {arXiv preprint arXiv:math/0701833},
  year   = {2010}
}

Comments

LATEX, 23 pages. To appear in the special issue of the Pure and Applied Mathematics Quarterly dedicated to F. Thomas Farrell and Lowell E. Jones

On the algebraic $L$-theory of $\Delta$-sets

Abstract

Keywords

Cite

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