Geodesic
Null-homologous exotic surfaces in 4–manifolds
Hoffman, Neil R1 ; Sunukjian, Nathan S2
1Department of Mathematics, Oklahoma State University, Stillwater, OK, United States
2Mathematics and Statistics Department, Calvin University, Grand Rapids, MI, United States
Algebraic and Geometric Topology, Tome 20 (2020) no. 5, pp. 2677-2685
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We exhibit infinite families of embedded tori in 4–manifolds that are topologically isotopic but smoothly distinct. The interesting thing about these tori is that they are topologically trivial in the sense that each bounds a topologically embedded solid handlebody. This implies that there are stably ribbon surfaces in 4–manifolds that are not ribbon.

DOI : 10.2140/agt.2020.20.2677
Classification : 57Q45, 57R40, 57R52, 57R57, 57M25
Keywords: ribbon surface, exotically embedded tori

Hoffman, Neil R  1   ; Sunukjian, Nathan S  2

1 Department of Mathematics, Oklahoma State University, Stillwater, OK, United States
2 Mathematics and Statistics Department, Calvin University, Grand Rapids, MI, United States 
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Hoffman, Neil R; Sunukjian, Nathan S. Null-homologous exotic surfaces in 4–manifolds. Algebraic and Geometric Topology, Tome 20 (2020) no. 5, pp. 2677-2685. doi: 10.2140/agt.2020.20.2677

[1] R I Baykur, N Sunukjian, Knotted surfaces in 4–manifolds and stabilizations, J. Topol. 9 (2016) 215 | DOI

[2] G Burde, H Zieschang, Knots, 5, de Gruyter (2003)

[3] R Fintushel, Knot surgery revisited, from: "Floer homology, gauge theory, and low-dimensional topology" (editors D A Ellwood, P S Ozsváth, A I Stipsicz, Z Szabó), Clay Math. Proc. 5, Amer. Math. Soc. (2006) 195

[4] R Fintushel, R J Stern, Surfaces in 4–manifolds, Math. Res. Lett. 4 (1997) 907 | DOI

[5] R Fintushel, R J Stern, Knots, links, and 4–manifolds, Invent. Math. 134 (1998) 363 | DOI

[6] T Kanenobu, H Murakami, Two-bridge knots with unknotting number one, Proc. Amer. Math. Soc. 98 (1986) 499 | DOI

[7] A Kawauchi, Ribbonness of a stable-ribbon surface-link, I: A stably trivial surface-link, preprint (2018)

[8] H J Kim, Modifying surfaces in 4–manifolds by twist spinning, Geom. Topol. 10 (2006) 27 | DOI

[9] H J Kim, D Ruberman, Smooth surfaces with non-simply-connected complements, Algebr. Geom. Topol. 8 (2008) 2263 | DOI

[10] H J Kim, D Ruberman, Topological triviality of smoothly knotted surfaces in 4–manifolds, Trans. Amer. Math. Soc. 360 (2008) 5869 | DOI

[11] T E Mark, Knotted surfaces in 4–manifolds, Forum Math. 25 (2013) 597 | DOI

[12] J M Montesinos, On twins in the four-sphere, I, Q. J. Math. 34 (1983) 171 | DOI

[13] J W Morgan, T S Mrowka, Z Szabó, Product formulas along T3 for Seiberg–Witten invariants, Math. Res. Lett. 4 (1997) 915 | DOI

[14] N S Sunukjian, Surfaces in 4–manifolds : concordance, isotopy, and surgery, Int. Math. Res. Not. 2015 (2015) 7950 | DOI

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