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- W3146492267 abstract "Let M i be a connected, compact, orientable 3-manifold, F i a boundary component of M i with g(F i ) 2, i = 1, 2, and F 1 ≌ F 2 . Let : F 1 → F 2 be a homeomorphism, and M = M 1 ∪ M 2 , F = F 2 = (F 1 ). Then it is known that g(M ) 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 i1 , Q i ) in (M i1 , F i ) satisfying χ(Q i ) 3 - 2g(M i ), i = 1, 2. Then g(M ) = g(M 1 ) + g(M 2 ) - g(F )." @default.
- W3146492267 created "2021-04-13" @default.
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- W3146492267 date "2010-01-01" @default.
- W3146492267 modified "2023-09-27" @default.
- W3146492267 title "A sufficient condition for the genus of an amalgamated 3-manifold not to go down" @default.
- W3146492267 hasPublicationYear "2010" @default.
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