Research Summary

Click here for a description of my research, past and present, and future intentions.

Preprints and publications

Click below to view my current papers and preprints

• Detecting Whitney disks for link maps in the four-sphere, J. Knot Theory Ramifications, Vol 26, Issue 12, 2017. (Mathscinet)

• On invariants of link maps in dimension four, J. Knot Theory Ramifications, Vol 25, Issue 11, 2016. (Mathscinet)

• The Schneiderman-Teichner invariant applied to immersions arising from link maps in ${S^4}$, Dec 2013, Preprint

Movies

Click below for "movies" of link maps $f:S_+^2\cup S^2_{{}_-}\to S^4$ with Kirk's $\sigma$-invariant having $\sigma_+(f)=0$. In each movie, Whitney disks for $f(S^2_+)$ in the complement of $f(S^2_{{}_-})$ are illustrated. The intersections between these Whitney disks and $f(S^2_+)$ are also shown, so that Li's secondary obstruction $\omega_+(f)$ can be computed.

• Animated movie of $\sigma(f) = (0, t^2-4t+3)$, $\omega_+(f)=1$
• Slideshow of $\sigma(f) = (0, t^9 - 9t+8)$, $\omega_+(f)=0$​