Publications and Preprints
Back to my research page.
Preprints
Here is the list of my preprints. You can download them as PDF files or gzipped PS files. Once ready for publication, my preprints will be posted on arXiv.
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Fox Re-embedding and Bing Submanifolds
preprint, October 2007 (updated on 6 Jan. 2008): PDF PS.GZAbstract: 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).
Note: This preprint is really a chapter of my thesis. My thesis did not contain figures, but I plan to add some figures. (19 Aug. 2008)
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The Girth-Alternative for Mapping Class Groups
preprint (under revision): e-mail me for a copyAbstract: The girth of a finitely generated group G is the supremum of the girth of Cayley graphs for G over all finite generating sets. We show that, for a compact orientable surface S, a finitely generated subgroup of the mapping class group Mod(S) is either a virtually abelian group or a non-cyclic group with infinite girth; moreover, these alternatives are mutually exclusive. The theorem can be regarded as a refinement of the Tits-alternative for subgroups of mapping class groups Mod(S) due to Ivanov (1984) and McCarthy (1985). The analogous refinement of the Tits-alternative for linear groups has already been established by Akhmedov (2005).
Note: This preprint is really a section from my Ph.D. thesis, and it will be reformatted before posted on arXiv. Please e-mail me for a copy. (19 Aug. 2008)