<oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title>On a move reducing the genus of a knot diagram</dc:title>
<dc:creator>Kenji Daikoku</dc:creator><dc:creator>Keiichi Sakai</dc:creator><dc:creator>Masamichi Takase</dc:creator>
<dc:subject>57M25</dc:subject><dc:subject>68R15</dc:subject><dc:subject>knot</dc:subject><dc:subject>canonical genus</dc:subject><dc:subject>bridge-replacing move</dc:subject><dc:subject>knotoid</dc:subject><dc:subject>virtual knot</dc:subject><dc:subject>Gauss diagram</dc:subject><dc:subject>Gauss code</dc:subject>
<dc:description>For a knot diagram we introduce an operation which does not increase the genus of the diagram and does not change its representing knot type. We also describe a condition for this operation to certainly decrease the genus. The proof involves the study of a relation between the genus of a virtual knot diagram and the genus of a knotoid diagram, the former of which has been introduced by Stoimenow, Tchernov, and Vdovina, and the latter by Turaev recently. Our operation has a simple interpretation in terms of Gauss codes and hence can easily be computer-implemented.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2012</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2012.61.4666</dc:identifier>
<dc:source>10.1512/iumj.2012.61.4666</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 61 (2012) 1111 - 1127</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>