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Representative Research Achievements

Periods of modular forms on Gamma(0) (N) and products of Jacobi theta functions

저자Author

YoungJu Choie

논문명Title

저널명Journal name

Journal of the European Mathematical Society

게재일Date of publication

2019

작성자Writer

관리자

작성일Date of issue

2020-06-05 16:57

Abstract

We prove that a Casson tower of height 4 contains a flat embedded disc bounded by the attaching circle, and we prove disc embedding results for height 2 and 3 Casson towers which are embedded into a 4-manifold, with some additional fundamental group assumptions. In the proofs we create a capped grope from a Casson tower and use a refined height raising argument to establish the existence of a symmetric grope which has two layers of caps, data which is sufficient for a topological disc to exist, with the desired boundary. As applications, we present new slice knots and links by giving direct applications of the disc embedding theorem to produce slice discs, without first constructing a complementary 4-manifold. In particular we construct a family of slice knots which are potential counterexamples to the homotopy ribbon slice conjecture.

https://link.springer.com/article/10.1007%2Fs00222-015-0639-z

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