Findings reveal that knot surgered elliptic surfaces for specific torus knots can be decomposed without certain handles, suggesting new insights into surface topology.
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.
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Monden et al. (2026) studied this question.
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