tag:blogger.com,1999:blog-52580734918948666172024-03-13T21:08:43.350-07:00Sketches of TopologyKen Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-5258073491894866617.post-29360504508191078652007-12-10T09:50:00.000-08:002007-12-10T09:52:09.914-08:00Moved to WordpressI've migrated this blog over to <a href="http://sketchesoftopology.wordpress.com">http://sketchesoftopology.wordpress.com</a>.Ken Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com0tag:blogger.com,1999:blog-5258073491894866617.post-36653813124649885132007-11-17T11:20:00.000-08:002007-11-26T17:52:27.299-08:00Contact structures: dz+xdy-ydx<a href="http://www.flickr.com/photos/17876350@N05/2040088913/" title="Contact structure dz+xdy-ydx v4 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2386/2040088913_ab65eafd75_m.jpg" width="240" height="171" alt="Contact structure dz+xdy-ydx v4" /></a><br /><br /><a href="http://www.flickr.com/photos/17876350@N05/2040088083/" title="Contact structure dz+xdy-ydx v3 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2199/2040088083_1f34ac1ec0_m.jpg" width="240" height="171" alt="Contact structure dz+xdy-ydx v3" /></a><br /><br />Some views of the planes in the kernel of the 1-form dz+xdy-ydxKen Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com0tag:blogger.com,1999:blog-5258073491894866617.post-40120855011566063062007-11-17T10:58:00.001-08:002007-11-17T10:59:53.636-08:00Cosmetic surgery on the Figure Eight Sister<style type="text/css">.flickr-photo { border: solid 2px #000000; }.flickr-yourcomment { }.flickr-frame { text-align: left; padding: 3px; }.flickr-caption { font-size: 0.8em; margin-top: 0px; }</style><div class="flickr-frame"> <a href="http://www.flickr.com/photos/17876350@N05/2040436061/" title="photo sharing"><img src="http://farm3.static.flickr.com/2057/2040436061_4cae8b54ec.jpg" width="400" class="flickr-photo" alt="" /></a><br /> <span class="flickr-caption"><a href="http://www.flickr.com/photos/17876350@N05/2040436061/">Cosmetic surgery on the Figure Eight Sister</a>, originally uploaded by <a href="http://www.flickr.com/people/17876350@N05/">epsilon_is_afraid_of_zeta</a>.</span></div> <p class="flickr-yourcomment"> The double branched cover of the closure of the braid on the left is the lens space L(5,1). The braid axis lifts to the Figure Eight Sister. Adding in two full twists downstairs is equivalent to doing +1 surgery on the knot up stairs. After braid moves, we obtain the mirror. <br /><br />Hence the figure eight sister exterior has two fillings yielding homeomorphic lens spaces.</p>Ken Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com0tag:blogger.com,1999:blog-5258073491894866617.post-59051642469221391232007-11-17T10:37:00.000-08:002007-11-27T08:53:06.428-08:00Scharlemann cycles<table><br /><tbody><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/1859286279/" title="longmobius34 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2095/1859286279_001c8f6b42_m.jpg" alt="longmobius34" width="180" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/1859282445/" title="extschcycle34 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2172/1859282445_3f3765f9ca_m.jpg" alt="extschcycle34" width="180" /></a><br /></td><br /></tr><br /><br /><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/1860113730/" title="longmobius25 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2156/1860113730_c4c325a1bb_m.jpg" alt="longmobius25" width="180" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/1860109726/" title="extschcycle25 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2203/1860109726_11fd3c1d9e_m.jpg" alt="extschcycle25" width="180" /></a><br /></td><br /></tr><br /><br /><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/1859288447/" title="longmobius16 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2138/1859288447_d5de91265e_m.jpg" alt="longmobius16" width="180" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/1860110598/" title="extschcycle16 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2005/1860110598_61fcc7db2a_m.jpg" alt="extschcycle16" width="180" /></a><br /></td><br /></tr><br /><br /><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/1859289783/" title="longmobius7t by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2354/1859289783_2a8535bf92_m.jpg" alt="longmobius7t" width="180" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/1859285383/" title="extschcycle7t by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2195/1859285383_beb2877cb0_m.jpg" alt="extschcycle7t" width="180" /></a><br /></td><br /></tr><br /></tbody></table>Ken Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com0tag:blogger.com,1999:blog-5258073491894866617.post-62991543552525941532007-11-17T10:21:00.000-08:002007-11-26T18:00:01.981-08:00Connect sum<table><br /><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040871608/" title="ConnectSum2U by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2014/2040871608_7e831c522d_m.jpg" width="180" alt="ConnectSum2U" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040077299/" title="ConnectSum2T by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2168/2040077299_59d30f8ab6_m.jpg" width="180" alt="ConnectSum2T" /></a><br /></td><br /></tr><br /></table><br /><br /><table><br /><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040861130/" title="ConnectSum0U by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2296/2040861130_71da6aeae1_m.jpg" width="180" alt="ConnectSum0U" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040861380/" title="ConnectSum0T by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2040/2040861380_6146b50ea6_m.jpg" width="180" alt="ConnectSum0T" /></a><br /></td><br /></tr><br /></table><br /><br /><table><br /><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040860408/" title="ConnectSum1U by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2309/2040860408_56fc642b58_m.jpg" width="180" alt="ConnectSum1U" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040860662/" title="ConnectSum1T by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2135/2040860662_854d00ffe5_m.jpg" width="180" alt="ConnectSum1T" /></a><br /></td><br /></tr><br /></table>Ken Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com0tag:blogger.com,1999:blog-5258073491894866617.post-25302691304244425122007-11-17T10:18:00.000-08:002007-11-27T08:35:39.313-08:00Blackboard pictures<a href="http://www.flickr.com/photos/17876350@N05/1860038394/" title="Photo 5 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2354/1860038394_f6b6e23fca.jpg" width="400" alt="Photo 5" /></a><br /><br /><a href="http://www.flickr.com/photos/17876350@N05/1859214635/" title="Photo 6 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2015/1859214635_52e8cd87aa.jpg" width="400" alt="Photo 6" /></a><br /><br /><a href="http://www.flickr.com/photos/17876350@N05/1860040094/" title="Photo 8 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2249/1860040094_8cd4786fbb.jpg" width="400" alt="Photo 8" /></a><br /><br /><a href="http://www.flickr.com/photos/17876350@N05/1859213121/" title="Photo 7 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2268/1859213121_5a7ae17b08.jpg" width="400" alt="Photo 7" /></a>Ken Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com1tag:blogger.com,1999:blog-5258073491894866617.post-61984623474981844272007-11-17T10:10:00.000-08:002007-11-27T08:49:21.214-08:00Grid diagram and trefoil<table><br /><tbody><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040895372/" title="Grid Trefoil by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2192/2040895372_e736a5c7ed_m.jpg" alt="Grid Trefoil" width="180" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040101819/" title="Grid Trefoil Tetra by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2364/2040101819_43420a40bc_m.jpg" alt="Grid Trefoil Tetra" width="180" /></a><br /></td><br /></tr><br /><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040102047/" title="Grid Trefoil Torus by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2228/2040102047_f33d96ce37_m.jpg" alt="Grid Trefoil Torus" width="180" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040101473/" title="Grid Trefoil Tetra Torus by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2419/2040101473_4eebfe5f12_m.jpg" alt="Grid Trefoil Tetra Torus" width="180" /></a><br /></td><br /></tr><br /></tbody></table><br /><table><br /><tbody><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040896028/" title="Side Trefoil by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2162/2040896028_b1c6e5dbc7_m.jpg" alt="Side Trefoil" width="180" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040896344/" title="Side Trefoil Tetra by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2221/2040896344_4206374ffc_m.jpg" alt="Side Trefoil Tetra" width="180" /></a><br /></td><br /></tr><br /><tr><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040102769/" title="Side Trefoil Torus by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2361/2040102769_c3e644156a_m.jpg" alt="Side Trefoil Torus" width="180" /></a><br /></td><br /><td><br /><a href="http://www.flickr.com/photos/17876350@N05/2040898264/" title="Side Trefoil Tetra Torus by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2103/2040898264_49645ebcd6_m.jpg" alt="Side Trefoil Tetra Torus" width="180" /></a><br /></td><br /></tr><br /></tbody></table>Ken Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com0tag:blogger.com,1999:blog-5258073491894866617.post-33477518386898078862007-11-17T10:01:00.000-08:002007-11-17T10:03:53.819-08:00Twisted Saddles<iframe align="center" src="http://www.flickr.com/slideShow/index.gne?user_id=17876350@N05&tags=saddles" frameBorder="0" "width=400" height="500" scrolling="no"></iframe>Ken Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com0tag:blogger.com,1999:blog-5258073491894866617.post-10811898001923874132007-11-17T09:50:00.000-08:002007-11-17T10:10:16.907-08:00Figure Eight and Braid<iframe align="center" src="http://www.flickr.com/slideShow/index.gne?user_id=17876350@N05&tags=figureeightknot" frameBorder="0" "width=400" height="500" scrolling="no"></iframe><br />Hmmm.... I'll have to figure out how to put these in the correct order.Ken Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com0tag:blogger.com,1999:blog-5258073491894866617.post-67253390384350921672007-11-17T09:15:00.001-08:002007-11-17T09:39:08.258-08:00Contact structure<style type="text/css">.flickr-photo { border: solid 2px #000000; }.flickr-yourcomment { }.flickr-frame { text-align: left; padding: 3px; }.flickr-caption { font-size: 0.8em; margin-top: 0px; }</style><div class="flickr-frame"> <a href="http://www.flickr.com/photos/17876350@N05/2040883920/" title="photo sharing"><img src="http://farm3.static.flickr.com/2111/2040883920_8b563a4eac.jpg" class="flickr-photo" alt="" /></a><br /> <span class="flickr-caption"><a href="http://www.flickr.com/photos/17876350@N05/2040883920/">ctctstr4</a>, originally uploaded by <a href="http://www.flickr.com/people/17876350@N05/">epsilon_is_afraid_of_zeta</a>.</span></div> <p class="flickr-yourcomment"> <br /><a href="http://www.flickr.com/photos/17876350@N05/2040883714/" title="ctctstr2 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2107/2040883714_5649f19b33_o.jpg" width="558" height="379" alt="ctctstr2" /></a><br /><a href="http://www.flickr.com/photos/17876350@N05/2040883558/" title="ctctstr3 by epsilon_is_afraid_of_zeta, on Flickr"><img src="http://farm3.static.flickr.com/2190/2040883558_e8e657f025_o.jpg" width="558" height="379" alt="ctctstr3" /></a><br /><br /><br />Here we see one view of some 2-planes of the standard contact structure.</p>Ken Bakerhttp://www.blogger.com/profile/08265646781045929554noreply@blogger.com0