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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Hadamard matrices and their designs: a coding-theoretic approach

Authors: E. F. Assmus and J. D. Key
Journal: Trans. Amer. Math. Soc. 330 (1992), 269-293
MSC: Primary 05B20; Secondary 05B05, 05B10, 94B25
MathSciNet review: 1055565
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Abstract: To every finite dimensional algebraic coefficient system (defined below) $ (\Theta,V)$ over the De Rham algebra $ \Omega (M)$ of a manifold $ M$, Sullivan builds a local system $ {\rho _\Theta }:{\pi _1}(M) \to V$, in the topological sense, such that the two cohomologies $ H_{{\rho _\Theta }}^{\ast}(M;V)$ and $ H_\Theta ^{\ast}(\Omega (M);V)$ are isomorphic. In this paper, if $ {\mathbf{K}}$ is a simplicial set and $ (\Theta,V)$ an algebraic system over the $ {C^\infty }$ forms $ {A_\infty }({\mathbf{K}})$, we prove a similar result. We use it to extend the Hirsch lemma to the case of fibration whose fiber is an Eilenberg-Mac Lane space with certain non nilpotent action of the fundamental group of the basis. We apply this to a model of the hyperbolic torus; different from the nilpotent one, this new model is a better mirror of the topology.

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Article copyright: © Copyright 1992 American Mathematical Society

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