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On a Theorem of Sullivan

Published online by Cambridge University Press:  20 November 2018

Michael A. Penna
Michael A. Penna*
Affiliation:
Department of Mathematical Sciences, I.U.P.U.I.Indianapolis, Indiana, U.S.A. 46205
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The purpose of this note is to give an elementary geometric proof of the following result stated by Sullivan (see (4)).

Theorem 1 (Sullivan). Let K be a finite simplicial complex with vertices v1, …, vN and corresponding barycentric coordinates b1, …, bN. Then the algebra of rational PL forms on K

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 2 , 01 June 1978 , pp. 201 - 206
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Bousfield, A. K., and Gugenheim, V. K. A. M., “On PL de Rham theory and rational homotopy type”, Memoirs of the A.M.S., 8 No. 179 (1976).Google Scholar
2. Kan, D. M., and Miller, E. Y., “Homotopy types and Sullivan's algebras of 0-forms”, Topology, 16 (1977), pp. 193-197.Google Scholar
3. Penna, M., “Differential geometry on simplicial spaces”, Transactions of the A.M.S., 214 (1975), pp. 303-323.Google Scholar
4. Sullivan, D., “Differential forms and the topology of manifolds”, Proceedings of Congress on Manifolds, Tokyo, Japan, 1973, pp. 37-49.Google Scholar