Dubrovnik VI – Geometric Topology September 30 – October 7, 2007
	ABSTRACTS	pdf-version of this abstract

Violeta Vasilevska
University of South Dakota, Vermillion, SD, USA

Shape fibrator properties of PL manifolds

Following the concept of the PL fibrator (introduced by Daverman), we introduce a new concept of a fibrator (by slightly changing the PL setting). We call a closed, orientable PL $n$-manifold N a codimension-$k$ shape m$_{\rm simpl}$(o)- fibrator if all proper, surjective PL maps $p:M \to B$, from any closed, (orientable) PL $(n+k)$-manifold $M$ to a simplicial triangulated manifold $B$, such that each point inverse has the same homotopy type as $N$, are approximate fibrations. Also we introduce a particular type of manifold called special manifold—closed manifold with a non-trivial fundamental group for which all self maps with non-trivial normal images on $\pi_1$-level are homotopy equivalences. First we shall address the following question: which special manifolds are shape m$_{\rm simpl}$o-fibrators (a codimension-$k$ shape m$_{\rm simpl}$o-fibrator for all $k$)? The main result states that every orientable, special PL $n$-manifold with non-trivial first homology group is a shape m$_{\rm simpl}$o-fibrator, if it is a codimension-2 shape m$_{\rm simpl}$o-fibrator. Next we shall discuss new result about homology $n$-spheres that are codimension-$(n+1)$ m$_{\rm simpl}$ fibrators.