论文标题
超组，Q系列和3个manifolds
Supergroups, q-series and 3-manifolds
论文作者
论文摘要
我们介绍了3个manifold不变性$ \ hat {z} $的超组类似物，也称为同源块，以前是普通紧凑型半充实的谎言组。我们专注于超级群体，并详细说明SU（2 | 1）的情况。从物理上讲，这些不变的人被实现为与五脑相交的五脑系统的BPS状态的索引。与原始情况一样，同源块是具有整数系数的Q系列。我们提供了一种明确的算法来计算一类钢管的3个manifolds的这些Q系，并研究了一些特定的3个杂志的量子模块和重新外观。最后，我们猜想了一个公式，该公式将$ \ hat {z} $不变式和量子不变式构建，该量子是由量子超级组的未经版本的非避免类别构建的。
We introduce supergroup analogues of 3-manifold invariants $\hat{Z}$, also known as homological blocks, which were previously considered for ordinary compact semisimple Lie groups. We focus on superunitary groups, and work out the case of SU(2|1) in details. Physically these invariants are realized as the index of BPS states of a system of intersecting fivebranes wrapping a 3-manifold in M-theory. As in the original case, the homological blocks are q-series with integer coefficients. We provide an explicit algorithm to calculate these q-series for a class of plumbed 3-manifolds and study quantum modularity and resurgence properties for some particular 3-manifolds. Finally, we conjecture a formula relating the $\hat{Z}$ invariants and the quantum invariants constructed from a non-semisimple category of representation of the unrolled version of a quantum supergroup.
