Vol. 77, No. 2, 1978

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On the geometry of combinatorial manifolds

Michael Anthony Penna

Vol. 77 (1978), No. 2, 499–522
Abstract

On a smooth manifold there are classical relations between vector fields and derivations of the smooth function algebra, and between differential forms and alternating linear maps of vector field tuples. In this paper similar relations are obtained for combinatorial manifolds. As an application of these results the existence of connexions and parallel translation on combinatorial manifolds is established.

Mathematical Subject Classification 2000
Primary: 57Q99
Secondary: 53C05
Milestones
Received: 12 May 1977
Published: 1 August 1978
Authors
Michael Anthony Penna