Trisections of surface complements and the Price twist

Kim, Seungwon¹ ; Miller, Maggie²

¹National Institute for Mathematical Sciences, Daejeon, South Korea, Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, Republic of Korea
²Department of Mathematics, Princeton University, Princeton, NJ, United States

Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 343-373

Résumé

Given a real projective plane S embedded in a 4–manifold X4 with Euler number 2 or − 2, the Price twist is a surgery operation on ν(S) yielding (up to) three different 4–manifolds: X4, τS(X4) and ΣS(X4). This is of particular interest when X4 = S4, as then ΣS(X4) is a homotopy 4–sphere which is not obviously diffeomorphic to S4. Here we show how to produce a trisection description of each Price twist on S ⊂ X4 by producing a relative trisection of X4 ∖ ν(S). Moreover, we show how to produce a trisection description of general surface complements in 4–manifolds.

Détail

DOI : 10.2140/agt.2020.20.343

Classification : 57M50, 57R65
Keywords: trisection, knotted surface, Price twist, surgery

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