Celebratio Mathematica — Gordon — Complete Bibliography

Complete Bibliography

Works connected to Kenneth Lee Baker

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K. L. Baker, C. Gordon, and J. Luecke: “Obtaining genus 2 Heegaard splittings from Dehn surgery,” Algebr. Geom. Topol. 13 : 5 (2013), pp. 2471–2634. MR 3116298 Zbl 1294.57013 article

John Edwin Luecke	Related
Kenneth Lee Baker	Related

K. L. Baker, C. Gordon, and J. Luecke: “Bridge number, Heegaard genus and non-integral Dehn surgery,” Trans. Am. Math. Soc. 367 : 8 (2015), pp. 5753–5830. MR 3347189 Zbl 1329.57017 ArXiv 1202.0263 article

John Edwin Luecke	Related
Kenneth Lee Baker	Related

K. L. Baker, C. Gordon, and J. Luecke: “Bridge number and integral Dehn surgery,” Algebr. Geom. Topol. 16 : 1 (2016), pp. 1–40. MR 3470696 Zbl 1339.57005 ArXiv 1303.7018 article

In a 3-manifold \( M \), let \( K \) be a knot and \( \hat{R} \) be an annulus which meets \( K \) transversely. We define the notion of the pair \( (R,\hat{K}) \) being caught by a surface \( Q \) in the exterior of the link \( K\cup\partial\hat{R} \). For a caught pair \( (\hat{R},K) \), we consider the knot \( K^n \) gotten by twisting \( K \) \( n \) times along \( \hat{R} \) and give a lower bound on the bridge number of \( K^n \) with respect to Heegaard splittings of \( M \)–as a function of \( n \), the genus of the splitting, and the catching surface \( Q \). As a result, the bridge number of \( K^n \) tends to infinity with \( n \). In application, we look at a family of knots \( \{K^n\} \) found by Teragaito that live in a small Seifert fiber space \( M \) and where each \( K^n \) admits a Dehn surgery giving \( S^3 \). We show that the bridge number of \( K^n \) with respect to any genus 2 Heegaard splitting of \( M \) tends to infinity with \( n \). This contrasts with other work of the authors as well as with the conjectured picture for knots in lens spaces that admit Dehn surgeries giving \( S^3 \).

John Edwin Luecke	Related
Kenneth Lee Baker	Related