A sufficient condition for the genus of an amalgamated 3-manifold not to go down

作者：Li FengLing^*; Yang GuoQiu; Lei FengChun

来源：Science China Mathematics, 2010, 53(7): 1697-1702.

DOI：10.1007/s11425-010-3130-8

• amalgamation
• essential surface
• Heegaard genus

Let M (i) be a connected, compact, orientable 3-manifold, F (i) a boundary component of M (i) with g(F (i) ) a (c) 3/4 2, i = 1, 2, and F (1) a parts per thousand S F (2). Let phi: F (1) -> F (2) be a homeomorphism, and M = M (1) a(phi)(a) M (2), F = F (2) = phi(F (1)). Then it is known that g(M) a (c) 1/2 g(M (1))+g(M (2))-g(F). In the present paper, we give a sufficient condition for the genus of an amalgamated 3-manifold not to go down as follows: Suppose that there is no essential surface with boundary (Q (i) , a,Q (i) ) in (M (i) , F (i) ) satisfying chi(Q (i) ) > 3 - 2g(M (i) ), i = 1, 2. Then g(M) = g(M (1)) + g(M (2)) - g(F).

• 出版日期2010-7
• 单位大连理工大学; 哈尔滨工业大学