Alexander's wild sphere [Archive]

Ulmo

Aug7-04, 05:05 PM

Marc Nardmann

Aug19-04, 12:36 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Ulmo wrote:\n\n> This is just wild speculation, but what would happen if in superstring\n> theory if you were to compactify the extra dimensions on Alexander\'s\n> wild sphere or horned sphere?\n\nI don\'t understand the question. What does it mean to "compactify the\nextra dimensions on Alexander\'s horned sphere"? Do you mean that the\nresult is a manifold of the form M x hornedsphere? First, the horned\nsphere is just a topological manifold, not a smooth manifold. Most\ntheories in physics (including string theory) deal with smooth\nmanifolds. Second, the horned sphere is homeomorphic to the standard\nsphere S^2. The only reason to consider the horned sphere is its\npeculiar imbedding in R^3. What role do you think the imbedding plays in\n"compactifying the extra dimensions on the horned sphere" (whatever that\nmeans)? Please explain.\n\n\n-- Marc Nardmann\n\nTo reply, remove every occurrence of a certain letter from my e-mail\naddress.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Ulmo wrote:

> This is just wild speculation, but what would happen if in superstring
> theory if you were to compactify the extra dimensions on Alexander's
> wild sphere or horned sphere?

I don't understand the question. What does it mean to "compactify the
extra dimensions on Alexander's horned sphere"? Do you mean that the
result is a manifold of the form M x hornedsphere? First, the horned
sphere is just a topological manifold, not a smooth manifold. Most
theories in physics (including string theory) deal with smooth
manifolds. Second, the horned sphere is homeomorphic to the standard
sphere S^2. The only reason to consider the horned sphere is its
peculiar imbedding in R^3. What role do you think the imbedding plays in
"compactifying the extra dimensions on the horned sphere" (whatever that
means)? Please explain.

-- Marc Nardmann

To reply, remove every occurrence of a certain letter from my e-mail
address.