论文标题
将通量同态扩展到具有量量的同态同态
Extending the flux homomorphism to volume-preserving homeomorphisms
论文作者
论文摘要
本文将通量同态扩展到具有量的同态同态。令人惊讶的$（C^0，δ） - $刚度结果，其中扩展的通量组与标准通量组一致。引入的工具还包括带有Fathi的质量流量的庞加莱二重性，以及对同构量的同质形态的规范，这表明具有同构行为的新灵活性。这种灵活性可能对刚性的刚性/宇宙几何形状产生影响，尤其是与Lefschetz歧管有关的几何形状：任何有限的能量符号符号同型同构为$（t^2，ω）$带有琐碎的磁通量，是有限的能量higemortonian pansomormormormormormormormormormormormormormormormormphism $（T^2^2，ω2，ω）$。我们讨论了$ h^\ ast（homeo_0（m，ω），\ Mathcal {c}（m，m，\ mathbb {r}））$ $ homeo_0（m，ω）$带系数的$ h^\ ast（homeo_0（m，ω））$ h^\ ast组$ h^\ ast（homeo_0（m，ω））$。
This paper extends the flux homomorphism to volume-preserving homeomorphisms. A surprising $(C^0, δ)-$rigidity result where the extended flux groups coincide with the standard flux group is proved. The introduced tools, which also include a Poincaré duality with Fathi's mass flow and a norm on the group of volume-preserving homeomorphisms, indicate a potential for new flexibility in the behavior of homeomorphisms. This flexibility could have implications for rigidity results in symplectic/cosymplectic geometry, particularly those concerning Lefschetz manifolds: Any finite energy symplectic homeomorphism of $(T^2, ω)$ with trivial flux, is a finite energy Hamiltonian homeomorphism of $(T^2, ω)$. We discuss the cohomology groups $H^\ast(Homeo_0(M,Ω), \mathcal{C}(M, \mathbb{R}) )$ of $ Homeo_0(M,Ω)$ with coefficients in $ \mathcal{C}(M, \mathbb{R})$.
