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On diffeomorphisms of 4-dimensional 1-handlebodies
We give a new proof of Laudenbach and Poénaru's theorem, which states that any diffeomorphism of the boundary of a 4-dimensional 1-handlebody extends to the whole handlebody. Our proof is based on the classification of Heegaard splittings of double handlebodies and a result of Cerf on diffeomorphism
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