论文标题
超扭转的连接总和的nu不变
Nu-invariants of extra-twisted connected sums
论文作者
论文摘要
我们分析了用渐近圆柱的calabi-yau歧管粘合圆圈产物的可能方法，以产生具有固体g_2的歧管，从而概括了Kovalev和Corti，Corti，Haskins，Haskins，Haskins，Nordström，Nordström，Pacini。然后，我们以FixPoint和Gluing贡献的方式表达了Crowley，Goette和NordströmArxiv的扩展NU-Invariant：1505.02734，其中包括不同类型的（广义）Dedekind总和。令人惊讶的是，计算涉及一些与Dedekind Eta功能特殊值和复杂乘法理论相关的非平凡的数字理论论证。我们计算的结果之一是，存在不是G_2-NullBordant的紧凑型G_2-manifolds。
We analyse the possible ways of gluing twisted products of circles with asymptotically cylindrical Calabi-Yau manifolds to produce manifolds with holonomy G_2, thus generalising the twisted connected sum construction of Kovalev and Corti, Haskins, Nordström, Pacini. We then express the extended nu-invariant of Crowley, Goette, and Nordström arXiv:1505.02734 in terms of fixpoint and gluing contributions, which include different types of (generalised) Dedekind sums. Surprisingly, the calculations involve some non-trivial number-theoretical arguments connected with special values of the Dedekind eta-function and the theory of complex multiplication. One consequence of our computations is that there exist compact G_2-manifolds that are not G_2-nullbordant.
