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
Abstract:
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 $M(F_g)$.
Results including:
(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.
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 $M(F_g)$.
Results including:
(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.
