A NOTE ON THE NIELSEN REALIZATION PROBLEM FOR K3 SURFACES

被引：7

作者：

Baraglia, David ^{[1
]}

Konno, Hokuto ^{[2
]}

机构：

[1] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

[2] Univ Tokyo, Grad Sch Math Sci, 3-8-1 Komaba, Meguro, Tokyo 1538914, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 09期

基金：

澳大利亚研究理事会;

关键词：

SEIBERG-WITTEN INVARIANTS; BAUER-FURUTA; FAMILIES; SMOOTH; TOPOLOGY; BUNDLES; ISOTOPY;

D O I：

10.1090/proc/15544

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We will show the following three theorems on the diffeomorphism and homeomorphism groups of a K3 surface. The first theorem is that the natural map ir0(Diff (K3))-+ Aut(H2(K3;Z)) has a section over its im-age. The second is that there exists a subgroup G of ir0(Dif f (K3)) of order two over which there is no splitting of the map Dif f (K3)-+ ir0(Dif f (K3)), but there is a splitting of Homeo(K3)-+ ir0(Homeo(K 3)) over the image of G in ir0(Homeo(K3)), which is non-trivial. The third is that the map ir1(Dif f (K3))-+ ir1(Homeo(K 3)) is not surjective. Our proof of these re-sults is based on Seib erg-Witten theory and the global Torelli theorem for K3 surfaces.

引用

页码：4079 / 4087

页数：9