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Fox reimbedding and Bing submanifolds | | Kei Nakamura
; | | Date: |
18 Feb 2012 | | Abstract: | Let M be an orientable closed connected 3-manifold. We introduce the notion
of amalgamated Heegaard genus of M with respect to a closed separating
2-manifold F, and use it to show that the following two statements are
equivalent: (i) a compact connected 3-manifold Y can be embedded in M so that
the exterior of the image of Y is a union of handlebodies; and (ii) a compact
connected 3-manifold Y can be embedded in M so that every knot in M can be
isotoped to lie within the image of Y .
Our result can be regarded as a common generalization of the reimbedding
theorem by Fox [Fox48] and the characterization of 3-sphere by Bing [Bin58], as
well as more recent results of Hass and Thompson [HT89] and Kobayashi and Nishi
[KN94]. | | Source: | arXiv, 1202.4062 | | Services: | Forum | Review | PDF | Favorites | |
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