9 papers
An irreducible real projective plane in the 4-sphere
Mark Hughes, Seungwon Kim, Maggie Miller +1
We construct an irreducible embedded projective plane in . This gives a counterexample to the Kinoshita conjecture and answers Problem 4.37 of the K3 problem list. Moreover, w…
Basepoints in Khovanov homology and nonorientable surfaces
Gheehyun Nahm
We enhance the Khovanov TQFT using basepoint actions, over the field with two elements. Our enhanced Khovanov TQFT behaves similarly to gauge/Floer theoretic invariants of the doub…
Knotting and linking in 4 and 5 dimensions from barbell diffeomorphisms
Seungwon Kim, Gheehyun Nahm, Alison Tatsuoka
In this paper, we construct infinitely many non-isotopic 3-knots in the 5-sphere, each of which has four critical points with respect to the standard height function of the 5-spher…
Brunnian links of 3-balls in the 4-sphere
Seungwon Kim, Gheehyun Nahm, Alison Tatsuoka
For each integer , we construct infinitely many -component Brunnian links of 3-balls in . Our main tool is the third author's result on the existence of splitting s…
The Rasmussen s-invariant and exotic 4-manifolds
Gheehyun Nahm
We give a short, analysis-free proof, inspired by Ren and Willis's, of the existence of exotic compact, orientable 4-manifolds. There are two distinguishing features of our proof.…
Rational surgery exact triangles in Heegaard Floer homology
Gheehyun Nahm
We construct a new family of surgery exact triangles in Heegaard Floer theory over the field with two elements. This family generalizes both Ozsváth and Szabó's - and -su…