论文标题
Hikami对统一的WRT不变性和假theta功能的观察
Hikami's observations on unified WRT invariants and false theta functions
论文作者
论文摘要
本文的目的是$ q $ series的家族，源自Habiro在Witten-Reshetikhin-Turaev不变的工作中。 $ q $ - 系列通常只有在$ q $是团结的根源时才有意义，但是对于某些情况，它还决定了开放单元光盘上的全态功能。这样的例子是Habiro的统一WRT不变性$ H（Q）$ forPoincaré同源性领域。 Hikami在2007年观察到了其在团结根基上的不连续性。更确切地说，$ h（ζ）$在统一根上的值为$ 1/2 $ $ h（q）$的限制值$ h（q）$ as $ q $倾向于$ζ$在单位光盘中径向放射线。在本文中，我们通过使用Bailey的引理和假theta功能理论来解释$ 1/2 $ -FACTOR的外观，并概括了Hikami的观察结果。
The object of this article is a family of $q$-series originating from Habiro's work on the Witten-Reshetikhin-Turaev invariants. The $q$-series usually make sense only when $q$ is a root of unity, but for some instances, it also determines a holomorphic function on the open unit disc. Such an example is Habiro's unified WRT invariant $H(q)$ for the Poincaré homology sphere. In 2007, Hikami observed its discontinuity at roots of unity. More precisely, the value of $H(ζ)$ at a root of unity is $1/2$ times the limit value of $H(q)$ as $q$ tends towards $ζ$ radially within the unit disc. In this article, we explain the appearance of the $1/2$-factor and generalize Hikami's observations by using Bailey's lemma and the theory of false theta functions.
