We compute the mapping class group of closed simply connected 6-manifolds M which look like complete intersections, that is, H2(M;Z)≅Z and x3≠0, where x∈H2(M;Z) is a generator. We determine some algebraic properties of the mapping class group; for example, we compute its abelianization and its center. We show that modulo the center the mapping class group is residually finite and virtually torsion-free. We also study low-dimensional homology groups. The results are very similar to the computation of the mapping class group of Riemann surfaces. We give generators of the mapping class group, and generators and relations for the subgroup acting trivially on π3(M).

Publication:

DUKE MATHEMATICAL JOURNAL

http://dx.doi.org/10.1215/00127094-2024-0036

Author:

Kreck

Mathematisches Institut Universität Bonn, Bonn, Germany, and Mathematisches Institut, Universität Frankfurt, Frankfurt, Germany

kreck@math.uni-bonn.de

Su

HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People’s Republic of China

suyang@math.ac.cn