| Popis: |
In this paper we use elementary combinatorial methods of PL topology to study the intersection of normal surfaces which are least weight in a homology class. Our point of view is that of Jaco and Rubinstein in which a theory of least weight normal surfaces is developed and used to give new proofs of the equivariant sphere theorem and the equivariant loop theorem. Our main result is a generalization of a theorem of Hass: If G is a group acting simplicially on a triangulated orientable 3-manifold M such that Fix(G) is a subcomplex and there exists a nontrivial element α in H2(M;Z) with g ∗ (α)=±α for each gϵG then there exists an equivariantly embedded normal surface F representing the homology class α. The proof of Hass relies on the differentiable theory of minimal surfaces while ours is a simple, self-contained topological proof. |
