ISSN:
1432-1785
Keywords:
Mathematics Subject Classification (1991):57N10, 57M50
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract: Every non-orientable 3-manifold M can be expressed as a union of three orientable handlebodies V 1,V 2,V 3 whose interiors are pairwise disjoint. If g i denotes the genus of ∂V i and g 3≤g 2≤g 3, then the tri-genus of M is the minimum triple (g 1,g 2,g 3), ordered lexicographically. If the Bockstein of the first Stiefel–Whitney class βw 1(M)=0, then M has tri-genus (0,2g,g 3), where g is the minimal genus of a 2-sided Stiefel Whitney surface of M. In this paper it is shown that, if βw 1(M)&\ne;0, then M has tri-genus (1,2g−1,g 3), where g is the minimal genus of a (1-sided) Stiefel–Whitney surface. As an application the tri-genus of certain graph manifolds is computed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002290050209
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