By constructing counterexamples,the authors show that the fixed subgroups are not compressed in direct products of free and surface groups,and hence negate a conjecture in[Zhang,Q.,Ventura,E.and J.Wu,Fixed subgroups a...By constructing counterexamples,the authors show that the fixed subgroups are not compressed in direct products of free and surface groups,and hence negate a conjecture in[Zhang,Q.,Ventura,E.and J.Wu,Fixed subgroups are compressed in surface groups,Internat.J.Algebra Comput.,25,2015,865–887].展开更多
Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold BM, and fπ ： π1 （M）→π1 （M） be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the...Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold BM, and fπ ： π1 （M）→π1 （M） be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of fπ, namely, rankFix（fπ） 〈 2rankπ1（M）, which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.展开更多
Let F be a finitely generated free group. Martino and Ventura gave an explicit description for the fixed subgroups of automorphisms of F. The author generalizes their results to injective endomorphisms.
基金supported by the National Natural Science Foundation of China(Nos.12271385,12471066)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(No.23JSY027)。
文摘By constructing counterexamples,the authors show that the fixed subgroups are not compressed in direct products of free and surface groups,and hence negate a conjecture in[Zhang,Q.,Ventura,E.and J.Wu,Fixed subgroups are compressed in surface groups,Internat.J.Algebra Comput.,25,2015,865–887].
基金Supported by NSFC(Grant No.11201364)"the Fundamental Research Funds for the Central Universities"
文摘Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold BM, and fπ ： π1 （M）→π1 （M） be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of fπ, namely, rankFix（fπ） 〈 2rankπ1（M）, which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.
基金supported by the National Natural Science Foundation of China(No.11201364)
文摘Let F be a finitely generated free group. Martino and Ventura gave an explicit description for the fixed subgroups of automorphisms of F. The author generalizes their results to injective endomorphisms.
