TY - JOUR

T1 - A complete description of normal surfaces for infinite series of 3-manifolds

AU - Fominykh, E. A.

PY - 2002/12/1

Y1 - 2002/12/1

N2 - The set of all normal surfaces in a 3-manifold is a partial monoid under addition with a minimal generating set of fundamental surfaces. The available algorithm for finding the system of fundamental surfaces is of a theoretical nature and admits no implementation in practice. In this article, we give a complete and geometrically simple description for the structure of partial monoids for normal surfaces in lens spaces, generalized quaternion spaces, and Stallings manifolds with fiber a punctured torus and a hyperbolic monodromy map.

AB - The set of all normal surfaces in a 3-manifold is a partial monoid under addition with a minimal generating set of fundamental surfaces. The available algorithm for finding the system of fundamental surfaces is of a theoretical nature and admits no implementation in practice. In this article, we give a complete and geometrically simple description for the structure of partial monoids for normal surfaces in lens spaces, generalized quaternion spaces, and Stallings manifolds with fiber a punctured torus and a hyperbolic monodromy map.

KW - Generalized quaternion space

KW - Lens space

KW - Normal surface

KW - Stallings manifold

UR - http://www.scopus.com/inward/record.url?scp=0036437101&partnerID=8YFLogxK

U2 - 10.1023/A:1021181720737

DO - 10.1023/A:1021181720737

M3 - Article

AN - SCOPUS:0036437101

VL - 43

SP - 1112

EP - 1123

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -