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.
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页码：4079 / 4087
页数：9
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