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CYLINDERS WITH COMPACT CROSS-SECTION AND THE STRIP CONJECTURE

The proof of the strip conjecture given just recently in [7] (see Theorem 3.1 below for a statement of the result) is best understood as a refinement of a proof of a general result for cylinders with compact cross-section (see Theorem 2.2 below). We elaborate on this statement. We give a detailed proof of Theorem 2.2 and we sketch a proof of Theorem 3.1. For a full proof of Theorem 3.1, we refer the reader to [7]. It should be noted that our proof of Theorem 2.2 is not the original proof given in [10, Th. 3], but rather it is a modification of an argument given even earlier in [3, Th. 5.1]. The content of this paper was presented in a series of two lectures in Séminaire de Structures Algébriques Ordonnées, Université Paris VI et VII in June 2008. The author wishes to thank the organizers F. Delon, M. Dickmann and D. Gondard for being allowed the opportunity to speak in the seminar and also to contribute to these seminar proceedings. It is hoped the paper serves some useful purpose in clarifying the proof of the strip conjecture in [7] and its relationship to [3, Th. 5.1] and [10, Th. 3].