论文标题
模量空间上奇异符号歧管和奇异形式的还原理论
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
论文作者
论文摘要
当所考虑的组是圆环时，对B-六歧管和折叠式歧管的对称性进行了研究（例如，对于b-晶格歧管，[gmps，glpr，gmw18a]）时，就可以理解。但是，还没有在这个领域中确定还原理论。除其他原因外，这是在[GMW18B，GMW21]中启动的这些流形的“减少量化通勤”程序中的基本基本。在本文中，我们填补了这一差距，并研究了一般$ b^m $ $ - 链状歧管和其他奇异符号歧管的一般对称性下的马斯登 - 温斯坦还原理论，包括某些折叠的符号歧管。在这个新框架中，一组可允许的哈密顿功能大于平滑函数的类别，因为它考虑了差异形式的奇异性。还考虑了准汉密尔顿的设置，并通过还原程序和融合产品获得（单数）准哈米顿空间的全新构建。
The investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds is well-understood when the group under consideration is a torus (see, for instance, [GMPS,GLPR, GMW18a] for b-symplectic manifolds and [CGP, CM] for folded symplectic manifolds). However, reduction theory has not been set in this realm in full generality. This is fundamental, among other reasons, to advance in the "quantization commutes with reduction" programme for these manifolds initiated in [GMW18b, GMW21]. In this article, we fill in this gap and investigate the Marsden-Weinstein reduction theory under general symmetries for general $b^m$-symplectic manifolds and other singular symplectic manifolds, including certain folded symplectic manifolds. In this new framework, the set of admissible Hamiltonian functions is larger than the category of smooth functions as it takes the singularities of the differential forms into account. The quasi-Hamiltonian set-up is also considered and brand-new constructions of (singular) quasi-Hamiltonian spaces are obtained via a reduction procedure and the fusion product.
