Subject: Subscribe and post (simultaneously!) From: David Roberts Date: Mon, 6 Sep 2004 15:16:52 +0930 To: dmd1@lehigh.edu I'm trying to find a non-orientable principal S1-bundle (E) over an orientable base space M of 'low' dimension (say 2-4). Here's the tricky bit: Want: H2(M) nontrivial - so we can twist the bundle. This is looking at a sort of generalisation of the nilmanifold of Scherk & Schwarz, i.e. the twisted torus with identifications (x,y,z)~(x,y+1,z)~(x,y,z+1) ~(x+1,y,z-jy) and metric ds2 = dx2 + dy2 + (dz + jxdy)2, to twisted _and_ non-orientable. Obviously we also need \pi_1(M) nontrivial so something with the homotopy equiv. to at least a circle, if not the join of two circles. The other alternative is if H2(M)=0, we have instead H3(E) nontrivial and hence M at least 3-dim'l. -- David Roberts Dept. Physics & Math. Physics Phone: 8303 3993 University of Adelaide South Australia, 5005 You know we all became mathematicians for the same reason: we were lazy. -Max Rosenlicht(1949) Also: droberts@physics.adelaide.edu.au hope.trf.org.au CRICOS Provider Number 00123M ----------------------------------------------------------- This email message is intended only for the addressee(s) and contains information that may be confidential and/or copyright. If you are not the intended recipient please notify the sender by reply email and immediately delete this email. Use, disclosure or reproduction of this email by anyone other than the intended recipient(s) is strictly prohibited. No representation is made that this email or any attachments are free of viruses. Virus scanning is recommended and is the responsibility of the recipient.