Abstract
Suppose a 2 2 -handle is attached to a compact orientable 3 3 -manifold M M along an annulus A A contained in a subsurface N N of ∂ M \partial M . If N N is compressible in M M , but N − A N - A is not, then the Thurston norm is unaffected. This generalizes a series of results due to Przytycki, Jaco, and Johannson.
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