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三次型、反常消解及模性(黄瑞芝)
2022-07-11 | 编辑:

   Motivated by the cubic forms and anomaly cancellation formulas of Witten-Freed-Hopkins, we give some new cubic forms on spin, spin^c, spin^{w_2} and orientable 12-manifolds respectively. We relate them to \eta-invariants when the manifolds are with boundary, and mod 2 indices on 10 dimensional characteristic submanifolds when the manifolds are spin^c or spin^{w_2}. Our method of producing these cubic forms is a combination of (generalized) Witten classes and the character of the basic representation of affine $E_8$.

    

  Publication: 

  Advances in Mathematics, Volume 394, 22 January 2022. 

    

  Author: 

  Fei Han 

  Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, 119076, Singapore 

  Email: mathanf@nus.edu.sg  

    

  Ruizhi Huang 

  Institute of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China 

  Email: huangrz@amss.ac.cn  

    

  Kefeng Liu 

  Department of Mathematics, University of California at Los Angeles, Los Angeles, CA 90095, USA 

  Mathematical Science Research Center, Chongqing University of Technology, Chongqing, 400054, China 

  Email: liu@math.ucla.edu  

    

  Weiping Zhang 

  Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, China 

  Email: weiping@nankai.edu.cn  

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