Seminars & Colloquia Calendar
Extending periodic maps on surfaces over the 4-sphere
Shicheng Wang (Peking University)
Location: Hill Center, Room 705
Date & time: Tuesday, 31 January 2023 at 4:00PM - 5:00PM
Seminar website: https://sites.google.com/view/rutgersgeometrytopologyseminar/home
Let \(F_g\) be the closed orientable surface of genus \(g\).
We address the problem to extend torsion elements of the mapping class group of \(M(F_g)\) over the 4-sphere \(S^4\).
Let \(w_g\) be a torsion element of maximum order in \(M(F_g)\).
(1) For each \(g\),
\(w_g\) is periodically extendable over \(S^4\) for some non-smooth embedding \(e: F_g\to S^4\), and not periodically extendable over \(S^4\) for any smooth embedding \(e: F_g\to S^4\).
(2) For each \(g\), \(w_g\) is extendable over \(S^4\) for some smooth embedding \(e: F_g\to S^4\)
if and only if \(g=4k, 4k+3\).
(3) For infinitely many primes, each periodic map of order \(p\) on \(F_g\) is extendable over \(S^4\) for some smooth embedding \(e: F_g\to S^4\).
This is a joint work with Zhongzi Wang.
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