n-knots in Sⁿ× S² and contractible (n+3)-manifolds

2023/06/10 by Geunyoung Kim, Kim, Geunyoung
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2306.06533

Abstract

In 1961, Mazur constructed a contractible, compact, smooth 4-manifold with boundary which is not homeomorphic to the standard 4-ball, using a 0-handle, a 1-handle and a 2-handle. In this paper, for any integer n≥2, we construct a contractible, compact, smooth (n+3)-manifold with boundary which is not homeomorphic to the standard (n+3)-ball, using a 0-handle, an n-handle and an (n+1)-handle. The key step is the construction of an interesting knotted n-sphere in Sⁿ× S² generalizing the Mazur pattern.

Related

• Exotic Mazur manifolds and knot trace invariants
• Mazur's knot and the Octahedron
• Knotted 3-balls in S⁴
• Some 4-manifold geometry from hyperbolic knots in S³
• Knotted handlebodies in the 4-sphere and 5-ball