Vol. 261, No. 1, 2013

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On slope genera of knotted tori in 4-space

Yi Liu, Yi Ni, Hongbin Sun and Shicheng Wang

Vol. 261 (2013), No. 1, 117–144
Abstract

We investigate genera of slopes of a knotted torus in the 4-sphere analogous to the genus of a classical knot. We compare various formulations of this notion, and use this notion to study the extendable subgroup of the mapping class group of a knotted torus.

Keywords
knotted surface, genus, extendable subgroup
Mathematical Subject Classification 2010
Primary: 57Q45
Secondary: 20F12
Milestones
Received: 7 December 2011
Revised: 9 September 2012
Accepted: 17 September 2012
Published: 28 February 2013
Authors
Yi Liu
Department of Mathematics
California Institute of Technology
374 Sloan Hall, 1200 East California Blvd
Pasadena, CA 91125
United States
Yi Ni
Department of Mathematics
California Institute of Technology
251 Sloan Hall, 1200 East California Blvd
Pasadena, CA 91125
United States
Hongbin Sun
Department of Mathematics
Princeton University
Fine Hall, Room 304
Washington Road
Princeton, NJ 08544
United States
Shicheng Wang
School of Mathematical Sciences
Peking University
Beijing, 100871
China