On knotted surfaces in $ R^4 $

Taubes, CliffordVafa, CumrunChen, Mingyue2021-07-1320212021-05-132021-05Chen, Mingyue. 2021. On knotted surfaces in $R^4$. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.28499474https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37368457In this article, we study surface knots, and propose some possible generalizations of the crossing changes in classical knot theory to the surface knot theory. In addition, we study the projections of surface knots into $R^3$ and discuss the double point sets in detail, along with the various moves.application/pdfenPhysicsOn knotted surfaces in $ R^4 $Thesis or Dissertation2021-07-130000-0003-2723-7705