Kei Nakamura’s talk on Oct. 28

Kei Nakamura will speak on October 28th in the Princeton Topology Seminar.

Title: Fox re-embedding and Bing submanifolds

Abstract: Let M be an orientable closed connected 3-manifold, and Y be a connected compact 3-manifold. We show that the following two conditions are equivalent: (i) Y can be embedded in M so that the closure of the complement of the image of Y is a union of handlebodies; and (ii) Y can be embedded in M so that every embedded closed loop in M can be isotoped to lie within the image of Y. Our result can be regarded as a common generalization of Fox’s reimbedding theorem (1948) and Bing’s characterization of 3-sphere (1958), as well as more recent results of Hass and Thompson (1989) and Kobayashi and Nishi (1994).

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