What do you call the product of a circle and an annulus? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T11:30:52Z http://mathoverflow.net/feeds/question/11307 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/11307/what-do-you-call-the-product-of-a-circle-and-an-annulus What do you call the product of a circle and an annulus? qwerty1793 2010-01-10T10:23:20Z 2010-02-09T17:50:50Z <p>What would you call the product of an annulus and \$S^1\$ (a 'thickened' torus like 3-manifold)?</p> <p>More generally, is there an archive or list online of names assigned to various (non-standard) manifolds by people? Or a set convention by which to name them?</p> http://mathoverflow.net/questions/11307/what-do-you-call-the-product-of-a-circle-and-an-annulus/11315#11315 Answer by Daniel Moskovich for What do you call the product of a circle and an annulus? Daniel Moskovich 2010-01-10T11:27:10Z 2010-01-10T13:59:43Z <p>I would call it a thickened torus. I don't know how standard that is, but it is quite normal to speak of thickened manifolds, where one means that manifold times a closed interval.<br> I have long felt that there should be a mathematical dictionary- not an encyclopaedia, by a dictionary- in order to fix and record standard usage.</p> http://mathoverflow.net/questions/11307/what-do-you-call-the-product-of-a-circle-and-an-annulus/14786#14786 Answer by ivane for What do you call the product of a circle and an annulus? ivane 2010-02-09T17:29:05Z 2010-02-09T17:50:50Z <p>that corresponds to the complement of a trivial (but essencial) torus knot in a open solid torus. For those -Fico had mention- they are called cable spaces and have nice foliation into circles. Its name is <strong>CS(1,0)</strong>. Can you see what is CS(2,1)?</p> <p>Edit at: utc-6 = 11:50 approx</p> <p>you could also say <strong>the trivial I-bundle over the torus</strong></p> http://mathoverflow.net/questions/11307/what-do-you-call-the-product-of-a-circle-and-an-annulus/14791#14791 Answer by Gerhard Paseman for What do you call the product of a circle and an annulus? Gerhard Paseman 2010-02-09T17:44:06Z 2010-02-09T17:44:06Z <p>May I {humbly} suggest "inner tube", as in "Floating down the river in an ... " ? (Strike while the terminological iron is hot.)</p> <p>Gerhard "Ask Me About System Design" Paseman, 2010.02.09</p>