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On graphs for
which every planar immersion lifts to a knotted spatial
embedding
Amy DeCelles, Joel Foisy, Chad Versace and Alice Wilson
Vol. 1 (2008), No. 2, 145–158
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Abstract |
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We call a graph intrinsically linkable if there is a way to assign over/under information to any planar immersion of such that the associated spatial embedding contains a pair of nonsplittably linked cycles. We define intrinsically knottable graphs analogously. We show there exist intrinsically linkable graphs that are not intrinsically linked. (Recall a graph is intrinsically linked if it contains a pair of nonsplittably linked cycles in every spatial embedding.) We also show there are intrinsically knottable graphs that are not intrinsically knotted. In addition, we demonstrate that the property of being intrinsically linkable (knottable) is not preserved by vertex expansion. |
Keywords
spatially embedded graph, intrinsically linked,
intrinsically knotted, regular projection
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Mathematical Subject Classification 2000
Primary: 57M25, 57M15
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Milestones
Received: 10 June 2007
Accepted: 1 December 2007
Published: 1 July 2008
Communicated by Ann Trenk
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Authors |
| Amy DeCelles | |
| Department of Mathematics University of Minnesota Minneapolis, MN 55455 United States |
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| Joel Foisy | |
| Department of Mathematics SUNY Potsdam Potsdam, NY 13676 United States |
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| http://www2.potsdam.edu/foisyjs/ | |
| Chad Versace | |
| Department of Mathematics University of South Alabama Mobile, AL 36688 United States |
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| Alice Wilson | |
| Department of Mathematics SUNY Potsdam Potsdam, NY 13676 United States |
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