STIEFEL-WHITNEY SURFACES AND DECOMPOSITIONS OF 3-MANIFOLDS INTO HANDLEBODIES
STIEFEL-WHITNEY SURFACES AND DECOMPOSITIONS OF 3-MANIFOLDS INTO HANDLEBODIES
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DOI：
10.1016/0166-8641(94)00018-2
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发表时间：
1994-12-14
影响因子：
0.6
通讯作者：
NUNEZ, V
中科院分区：
文献类型：
--
作者：
GOMEZLARRANAGA, C;HEIL, W;NUNEZ, V
每一个闭的不可定向3-流形M都可以作为三个内部两两不相交的可定向可定向体V1，V2，V3的并而得到。如果g（i）表示V（i）的亏格，g1小于或等于g2小于或等于g3，我们说M有三亏格（g1，g2，g3），如果根据字典序，三元组（g1，g2，g3）在M到可定向可分体的所有这样的分解中是最小的。我们将M的三亏格与表示M的第一Stiefel-Whitney类的对偶的曲面的亏格联系起来。这用于确定g1和g2。
Every closed nonorientable 3-manifold M can be obtained as the union of three orientable handlebodies V1, V2, V3 whose interiors are pairwise disjoint. If g(i) denotes the genus of V(i), g1 less-than-or-equal-to g2 less-than-or-equal-to g3, we say that M has tri-genus (g1, g2, g3), if in terms of lexicographical ordering, the triple (g1, g2, g3) is minimal among all such decompositions of M into orientable handlebodies. We relate the tri-genus of M to the genus of a surface that represents the dual of the first Stiefel-Whitney class of M. This is used to determine g1 and g2.