Jim Stasheff: I will survey the definitions and main results without proofs, including fiber bundles, transition functions, universal bundles, classifying spaces, characteristic classes and the covering homotopy property (CHP).

Mark Macerto and Aakash Parikh: One of the clearest patterns amongst the higher homotopy groups of spheres is stability along diagonals. Namely, if k > 0 is fixed, then the sequence of groups  pi_(k+i) S^i  becomes constant for sufficiently large i. This pattern is a special case of a more general phenomenon, which is described by the Freudenthal Suspension Theorem. We will describe some of the basics of homotopy theory, give a proof of the theorem, and discuss some applications.

96

Normal
0

false
false
false

EN-US
X-NONE
X-NONE

/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:12.0pt;
font-family:Calibri;
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;}