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STEPHEN D. THERIAULT - A reconstruction of Anick's fibration $S^{2n-1}\longrightarrow T^{2n-1}(p^{r})\longrightarrow \Omega S^{2n+1}$



STEPHEN D. THERIAULT, Department of Mathematics, MIT, Cambridge, MA, 02139, USA
A reconstruction of Anick's fibration $S^{2n-1}\longrightarrow T^{2n-1}(p^{r})\longrightarrow \Omega S^{2n+1}$


Let p be an odd prime and $r\geq 1$.

A long standing conjecture in homotopy theory was the existence of a fibration $S^{2n-1}\longrightarrow T^{2n-1}(p^{r})\longrightarrow \Omega S^{2n+1}$whose boundary map is degree pr on the bottom cell. Recent work of Anick proved that such a fibration exists for primes $p\geq 5$. However, his construction is extremely complex and this hinders one from learning any more about the properties of the space T2n-1(pr). I will present a new construction of the fibration which is much simpler, holds for all odd primes, and allows one to positively resolve many of the conjectures regarding the properties of the space T2n-1(pr).


 
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