Membranes in the product of a surface and a circle
by
Zbigniew Karno
Institute of Math., University of Bialystok

Let M be a surface (i.e., two-dimensional compact connected manifold). Let p : M ×S¹ --> M and q : M ×S¹ --> S¹ be the projections of M ×S¹ to M and the circle S¹, respectively. In our talk we show that if M is different from a disk, a sphere and a projective plane, then there exist two disjoint membranes P and A in M ×S¹ for p and q, respectively. In the construction, P is a surface and A is a circle. Related constructions with additional properties will be also discussed.

Here by a membrane of a mapping f:X --> N of a space X to a compact manifold N we mean any subset C subset K such that the restriction f|_C : C --> N is essential, i.e., for any mapping g:C --> N which is homotopic to f|_C relatively C \cap f^-1(\partialN) we have g(C) = N.

Date received: May 14, 1998