New York Journal of Mathematics
Volume 27 (2021), 1439-1442


Stanislav Jabuka

Periodic spanning surfaces of periodic knots

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Published: October 1, 2021.
Keywords: Knots, Spanning surfaces for knots, Nonorientable surfaces.
Subject: 57M25, 57M27.

It is a well-known result by Edmonds that every periodic knot of genus g bounds an equivariant Seifert surface of genus g. We show that this is not true if one instead considers nonorientable spanning surfaces of a periodic knot. We demonstrate by example that the difference between the first Betti number of an equivariant and a nonequivariant nonorientable spanning surface of a periodic knot, can be arbitrarily large.


The author was partially supported by the Simons Foundation, Award ID 524394, and by the NSF, Grant No. DMS-1906413.

Author information

Stanislav Jabuka:
Department of Mathematics and Statistics
University of Nevada
Reno NV 89557, USA