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Title: Tri-plane diagrams for simple surfaces in S4
Meier and Zupan proved that an orientable surface [Formula: see text] in [Formula: see text] admits a tri-plane diagram with zero crossings if and only if [Formula: see text] is unknotted, so that the crossing number of [Formula: see text] is zero. We determine the minimal crossing numbers of nonorientable unknotted surfaces in [Formula: see text], proving that [Formula: see text], where [Formula: see text] denotes the connected sum of [Formula: see text] unknotted projective planes with normal Euler number [Formula: see text] and [Formula: see text] unknotted projective planes with normal Euler number [Formula: see text]. In addition, we convert Yoshikawa’s table of knotted surface ch-diagrams to tri-plane diagrams, finding the minimal bridge number for each surface in the table and providing upper bounds for the crossing numbers.  more » « less
Award ID(s):
2005518
PAR ID:
10428663
Author(s) / Creator(s):
; ; ; ; ; ; ; ; ; ;
Date Published:
Journal Name:
Journal of Knot Theory and Its Ramifications
ISSN:
0218-2165
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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