【学术报告】Extending periodic maps on surfaces over the 4-sphere

• 主讲人：Prof. Shicheng Wang, Peking University
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2022-04-07 20:00 - 2022-04-07 21:00
• 地点： online

Video: https://disk.pku.edu.cn:443/link/C745583AE3B73B5E4E69ABDBAE6C8459
Valid Until: 2026-05-31 23:59

 

Abstract: The topic indicated by the title has been addressed by Montesinos (1982) and Hirose (2002) using Rohlin intersection form, and by Ding-Liu-Wang-Yao (2012) using spin structures.

    Based on the work above, we deduce a more computable criterion for extending periodic maps on surfaces over the 4-sphere.

    Some applications are given. Results including:

(1) Let $F_g$ be the closed orientable surface of genus $g$ and $w_g$ be a periodic map of maximum order on $F_g$.

    Then $w_g$ is extendable over $S^4$ for some smooth embedding $e: F_g\ to S^4$ if and only if $g=4k, 4k+3$.

(2) For infinitely many primes $p$, 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 joint work with Zhongzi Wang.

 

Bio: Prof. Shicheng Wang is currently a Distinguished Professor at the Department of Mathematics, Peking University. He received a master's degree from Peking University in 1981 and a doctorate degree from UCLA in 1988. He has won the Shiing-Shen Chern Mathematics Award and the second prize of the National Natural Science Awards (China). Prof. Wang was an invited speaker at the ICM’2002 in Beijing. His research focuses on low-dimensional topology, involving geometric group theory, dynamical systems, and algebraic topology.