Embedding Seifert manifolds in S^4

On the intersection forms of spin four-manifolds with boundary

“…This method can be refined by choosing X to be an orbifold rather than a manifold, and applying the orbifold version of (2) developed by Fukumoto and Furuta in [16]. We refer to [5,15,8] for some results obtained using these methods.…”

Embeddings of 3-Manifolds in S4 from the Point of View of the 11-Tetrahedron Census

“…(3) (2,3,13) or (2,5,7) (4) (2,5,9) or (3,4,7) Proof Casson and Harer prove that these Brieskorn spheres Σ bound contractible 4-manifolds M where M has a handle decomposition with a single 0, 1 and 2-handle, and no 3 or 4-handles. Thus the corresponding handle decomposition for M × I can be trivialized via handle-slides, making M a smooth submanifold of…”

“…This led to one of the more interesting conjectures about 3-manifolds embedding in S 4 , due to Gilmer and Livingston [21] concerning when a connect-sum of two lens spaces embeds in S 4 . The Gilmer-Livingston conjecture was solved by Fintushel and Stern [18], and recently generalized by Andrew Donald [13] to the case of an arbitrary connect-sum of lens spaces.…”

Distinguishing topologically and smoothly doubly slice knots

“…Let d(M, s) denote the correction term associated to the pair (M, s). The main tool in this paper is the following theorem, which also appears in [Don12] and [GL83] in one form or another.…”

“…In this subsection we will present a sufficient condition for a knot K to be doubly slice that applies when K is obtained by a certain type of infection. We remark that Donald [Don12] gives a different sufficient condition: one which involves systems of ribbon bands for K.…”