Families of diffeomorphisms and concordances detected by trivalent graphs
Families of diffeomorphisms and concordances detected by trivalent graphs
复制标题
通过三价图检测的微分同态和一致性家族
DOI：
10.1112/topo.12283
复制
发表时间：
2023
影响因子：
1.1
通讯作者：
Watanabe Tadayuki
中科院分区：
文献类型：
--
作者：
Botvinnik Boris;Watanabe Tadayuki
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∗(BDiff∂(Dd))⊗Q$\pi _*(B\mathrm{Diff}_{\partial }(D^d))\otimes {\mathbb {Q}}$ are lifted to homotopy groups of the moduli space of h$h$‐cobordisms π∗(BDiff⊔(Dd×I))⊗Q$\pi _*(B\mathrm{Diff}_{\sqcup }(D^d\times I))\otimes {\mathbb {Q}}$. As a geometrical application, we show that those elements in π∗(BDiff∂(Dd))⊗Q$\pi _*(B\mathrm{Diff}_{\partial }(D^d))\otimes {\mathbb {Q}}$ for d⩾4$d\geqslant 4$ are also lifted to the rational homotopy groups π∗(M∂psc(Dd)h0)⊗Q$\pi _*(\mathcal {M}^\mathsf {psc}_{\partial }(D^d)_{h_0})\otimes {\mathbb {Q}}$ of the moduli space of positive scalar curvature metrics. Moreover, we show that the same elements come from the homotopy groups π∗(M⊔psc(Dd×I;g0)h0)⊗Q$\pi _*(\mathcal {M}^\mathsf {psc}_{\sqcup } (D^d\times I; g_0)_{h_0})\otimes {\mathbb {Q}}$ of moduli space of concordances of positive scalar curvature metrics on Dd$D^d$ with fixed‐round metric h0$h_0$ on the boundary Sd−1$S^{d-1}$.
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∗(BDiff∂(Dd))⊗Q$\pi _*(B\mathrm{Diff}_{\partial }(D^d))\otimes {\mathbb {Q}}$ are lifted to homotopy groups of the moduli space of h$h$‐cobordisms π∗(BDiff⊔(Dd×I))⊗Q$\pi _*(B\mathrm{Diff}_{\sqcup }(D^d\times I))\otimes {\mathbb {Q}}$. As a geometrical application, we show that those elements in π∗(BDiff∂(Dd))⊗Q$\pi _*(B\mathrm{Diff}_{\partial }(D^d))\otimes {\mathbb {Q}}$ for d⩾4$d\geqslant 4$ are also lifted to the rational homotopy groups π∗(M∂psc(Dd)h0)⊗Q$\pi _*(\mathcal {M}^\mathsf {psc}_{\partial }(D^d)_{h_0})\otimes {\mathbb {Q}}$ of the moduli space of positive scalar curvature metrics. Moreover, we show that the same elements come from the homotopy groups π∗(M⊔psc(Dd×I;g0)h0)⊗Q$\pi _*(\mathcal {M}^\mathsf {psc}_{\sqcup } (D^d\times I; g_0)_{h_0})\otimes {\mathbb {Q}}$ of moduli space of concordances of positive scalar curvature metrics on Dd$D^d$ with fixed‐round metric h0$h_0$ on the boundary Sd−1$S^{d-1}$.
登录
查看更多内容
DOI：
10.2140/involve.2020.13.51
发表时间：
2020
期刊：
arXiv: Algebraic Topology
影响因子：
--
作者：
A. Kupers;O. Randal
通讯作者：
O. Randal
DOI：
10.1515/9781400878055
发表时间：
1965
期刊：
--
影响因子：
--
作者：
J. Milnor
通讯作者：
J. Milnor
Seiberg-Witten 方程组的正标量曲率和高维族
DOI：
--
发表时间：
2022
期刊：
影响因子：
--
作者：
Marui I.;Fukisaw A.; Nagashima Y.、Moon C.、Yamasaki K.;Inagaki S.、and Yamada T.;今野北斗
通讯作者：
今野北斗
勘误表：关于 Kontsevich 高维球丛的特征类 II：更高类
影响因子：
1.1
作者：
Shoichi Fujimori;Yu Kawakami;Masatoshi Kokubu; Wayne Rossman;Masaaki Umehara;Kotaro Yamada and Seong-Deog Yang;石井敦;久本智之;Watanabe Tadayuki
通讯作者：
Watanabe Tadayuki
三叶草微积分和 3 流形的有限类型不变量
影响因子：
2
作者：
S. Garoufalidis;M. Goussarov;M. Polyak
通讯作者：
M. Polyak