First cohomology of pure mapping class groups of big genus one and zero surfaces

被引：0

作者：

Domat, Gorge ^{[1
]}

Plummer, Paul ^{[2
]}

机构：

[1] Univ Utah, Dept Math, Salt Lake City, UT 84102 USA

[2] Univ Oklahoma, Dept Math, Norman, OK 73109 USA

来源：

NEW YORK JOURNAL OF MATHEMATICS | 2020年 / 26卷

关键词：

infinite-type surface; big mapping class groups; group cohomology; polish groups; automatic continuity;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the first integral cohomology of pure mapping class groups of infinite type genus one surfaces is trivial. For genus zero surfaces we prove that not every homomorphism to Z factors through a sphere with finitely many punctures. In fact, we get an uncountable family of such maps.

引用

页码：322 / 333

页数：12

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