Stable Maps of 3-manifolds into the Plane and Their Quotient Spaces
نویسندگان
چکیده
We study stable maps / : M —*U of closed orientable 3-manifolds M into the plane using their quotient spaces, which are defined to be the spaces of the connected components of/-fibres and which are known to be 2-dimensional polyhedra. We show that every 3-manifold admits a stable map whose quotient space is homeomorphic to that of a stable map of 5 \ We also deduce a Morse-type inequality for stable maps, which implies that there is no universal stable map of 5 in the above sense. Certain moves in the quotient spaces corresponding to generic homotopies of stable maps are also studied.
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