Ash Lightfoot
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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 $\sigma(f) = (0, t^9 - 9t+8)$, $\omega_+(f)=0$​
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  • Home
  • Research
  • Teaching
  • Curriculum Vitae
  • Seminars