Springer Science and Business Media LLC Acta Medica Okayama 0046-5755 220 3 2026 Knot surgered elliptic surfaces without 1- and 3-handles for a (2, 2h + 1)-torus knot 29 EN Naoyuki Monden Department of Mathematics, Faculty of Science, Okayama University Reo Yabuguchi Department of Mathematics, Faculty of Science, Okayama University For any positive integers h and n, we show that a knot surgered elliptic surface E(n)T(2,2h+1) for a (2, 2h + 1)-torus knot T (2, 2h + 1) admits a handle decomposition without 1- and 3-handles using a Kirby diagram derived from a Lefschetz fibration on it. As a corollary, an elliptic surface E(1)2,2h+1 has such a handle decomposition. No potential conflict of interest relevant to this article was reported.

Wiley Acta Medica Okayama 0024-6107 100 3 2019 Signatures of surface bundles and scl of a Dehn twist 957 986 EN Naoyuki Monden Department of Mathematics, Faculty of Science, Okayama University The first aim of this paper is to give four types of examples of surface bundles over surfaces with non-zero signature. The first example is with base genus 2, a prescribed signature, a 0-section and the fiber genus greater than a certain number which depends on the signature. This provides a new upper bound on the minimal base genus for fixed signature and fiber genus. The second example gives a new asymptotic upper bound for this number in the case that fiber genus is odd. The third example has a small Euler characteristic. The last is a non-holomorphic example. The second aim is to improve upper bounds for stable commutator lengths of Dehn twists by giving factorizations of powers of Dehn twists as products of commutators. One of the factorizations is used to construct the second examples of surface bundles. As a corollary, we see that there is a gap between the stable commutator length of the Dehn twist along a non-separating curve in the mapping class group and that in the hyperelliptic mapping class group if the genus of the surface is greater than or equal to 8. No potential conflict of interest relevant to this article was reported.