This is yours truly. Hello everyone .
The picture above was taken on March 1968. From left to right, Steven Vagi, Michael Wichman, Yuen Fat Wong, and Harry Miller, four big shots of the department in the old days. Steven has retired, Michael is pursing his wealth, and Yuen Fat is in a retirement program now and Harry is a department chair at an university somewhere in Kentucky.
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Hi, Everyone
I want to share with you a classical theorem of Lens Space.
Namely, L(m,p) is homotopic to L(m,q) iff there is a k mod m such as in a statement (see) below.
If you can fill in the whole proof, it would be quite interesting an undertaking.
For example, It was a very interesting question to ask when two lens space L(m,p)
and L(m,q)are homotopic? (cf. Whitehead) Yes, if p = k^(2)*q Mod m
such k,integer exists, ^(2) means square.
For example: If you can figure out their cell structures (from definition alone)
and their boundary maps and set up a chain homotopy to connect them
even better.(cf. Milnor, Whitehead Torsons)
For example: How about group = (cyclic)Z(m) actions on these homotopic spheres ?
(cf. Browder)
HAVE A NICE DAY (may 1, 2006, Yuen F. Wong)
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