Surfaces in D⁴ with the same boundary and fundamental group

2017/08/08 by Oba, Takahiro
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1708.02523

Abstract

We construct a family of pairs of non-isotopic symplectic surfaces in the standard symplectic 4-disk such that they are bounded by the same transverse knot in the standard contact 3-sphere and fundamental groups of their complements are isomorphic. In the appendix, we prove explicitly that one can obtain a symplectic surface in the standard symplectic 4-disk from a braided surface in a bidisk.

Related

• Symplectic surfaces and bridge position
• The Isotopy Problem for Symplectic 4-manifolds
• Ruled 4-manifolds and isotopies of symplectic surfaces
• Non-isotopic Seifert surfaces in the 4-ball
• Knotted surfaces with simply-connected complements