# The Homotopy-Fibre of the Double Suspension $E^2:S^{2n-1}\to\Omega^2 S^{2n+1}$

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Paul Selick, University of Toronto

Zoom link: https://princeton.zoom.us/j/96282936122

Passcode: 998749

The double suspension $E^2:S^{2n-1}\to\Omega^2 S^{2n+1}$ plays a key role in understanding the homotopy theory of spheres and related spaces. There are a number of interesting questions concerning its homotopy fibre including both many that have been resolved and many that have resisted solution for $60$ years since they were proposed.

This talk will discuss what progress has been made in understanding the double suspension and describe many open questions concerning it.