论文标题
通过三价图检测到的差异和一致性的家族
Families of diffeomorphisms and concordances detected by trivalent graphs
论文作者
论文摘要
我们研究了通过Kontsevich类检测到的三价图检测到的差异的家族。我们指定了第二名作者的一些最新结果和构造，以表明同型组中的那些非平凡元素$π_*（b \ mathrm {diff} _ {\ partial}（d^d）（d^d））\ otimes \ otimes \ mathbb {q} $ {q} $由$ h $ -H $ -H $ -H $ -H $ -H $ -COB提升为$π_*（B \ Mathrm {diff} _ {\ sqcup}（d^d \ times i））\ otimes \ mathbb {q} $。作为几何应用，我们表明$π_*中的那些元素（b \ m \ mathrm {diff} _ {\ partial}（d^d）（d^d））\ otimes \ otimes \ mathbb {q} $ for $ d \ geq 4 $也被提升为合理同型组$π_*（\ Mathcal {M}^{\ Mathrm {psc}} _ {\ partial}（d^d）_ {h_0}）\ otimes \ otimes \ otimes \ Mathbb {q} $ supar曲线的Moduli空间。此外，我们表明相同的元素来自同质组$π_*（\ Mathcal {M}^{\ Mathrm {\ Mathrm {psc}} _ {\ sqcup}（\ sqcup}（d^d \ times I; g_0; g_0; g_0）_ {h_0}）_ {h_0}） $ d^d $上的指标，带固定的圆形公制$ h_0 $在边界$ s^{d-1} $上。
We study families of diffeomorphisms detected by trivalent graphs via the Kontsevich classes. We specify some recent results and constructions of the second named author to show that those non-trivial elements in homotopy groups $π_*(B\mathrm{Diff}_{\partial}(D^d))\otimes \mathbb{Q}$ are lifted to homotopy groups of the moduli space of $h$-cobordisms $π_*(B\mathrm{Diff}_{\sqcup}(D^d\times I))\otimes \mathbb{Q}$. As a geometrical application, we show that those elements in $π_*(B\mathrm{Diff}_{\partial}(D^d))\otimes \mathbb{Q}$ for $d\geq 4$ are also lifted to the rational homotopy groups $π_*(\mathcal{M}^{\mathrm{psc}}_{\partial}(D^d)_{h_0})\otimes \mathbb{Q}$ of the moduli space of positive scalar curvature metrics. Moreover, we show that the same elements come from the homotopy groups $π_*(\mathcal{M}^{\mathrm{psc}}_{\sqcup} (D^d\times I; g_0)_{h_0})\otimes \mathbb{Q}$ of moduli space of concordances of positive scalar curvature metrics on $D^d$ with fixed round metric $h_0$ on the boundary $S^{d-1}$.
