It is already known that finitely-generated Fuchsian groups are profinitely rigid among all lattices of connected Lie groups by the result of Bridson,Conder and Reid.Hence the triangle groups are distinguished among t...It is already known that finitely-generated Fuchsian groups are profinitely rigid among all lattices of connected Lie groups by the result of Bridson,Conder and Reid.Hence the triangle groups are distinguished among themselves by their finite quotients.We focus on the question about quantifying the size of a quotient which separates two triangle groups and give an explicit upper bound.展开更多
For any pair of orientable closed hyperbolic 3-manifolds,this paper shows that any isomorphism between the profinite completions of their fundamental groups witnesses a bijective correspondence between the Zariski den...For any pair of orientable closed hyperbolic 3-manifolds,this paper shows that any isomorphism between the profinite completions of their fundamental groups witnesses a bijective correspondence between the Zariski dense PSL(2,Q^(ac))-representations of their fundamental groups,up to conjugacy;moreover,corresponding pairs of representations have identical invariant trace fields and isomorphic invariant quaternion algebras.(Here,Q^(ac)denotes an algebraic closure of Q.)Next,assuming the p-adic Borel regulator injectivity conjecture for number fields,this paper shows that uniform lattices in PSL(2,C)with isomorphic profinite completions have identical invariant trace fields,isomorphic invariant quaternion algebras,identical covolume,and identical arithmeticity.展开更多
Surface bundles arising from periodic mapping classes may sometimes have non-isomorphic, but profinitely isomorphic fundamental groups. Pairs of this kind have been discovered by Hempel. This paper exhibits examples o...Surface bundles arising from periodic mapping classes may sometimes have non-isomorphic, but profinitely isomorphic fundamental groups. Pairs of this kind have been discovered by Hempel. This paper exhibits examples of nontrivial Hempel pairs where the mapping tori can be distinguished by some Turaev-Viro invariants, and also examples where they cannot be distinguished by any Turaev-Viro invariants.展开更多
Let X and Y be connected nilpotent CW-complexes of finite type. In this paper we deal with another complete analysis of a set of phantom maps in terms of strong homology by using the derived functors. We also prove th...Let X and Y be connected nilpotent CW-complexes of finite type. In this paper we deal with another complete analysis of a set of phantom maps in terms of strong homology by using the derived functors. We also prove that the set of homotopy classes of maps is independent of the choice of both rational homotopy equivalent classes and completion genera.展开更多
文摘It is already known that finitely-generated Fuchsian groups are profinitely rigid among all lattices of connected Lie groups by the result of Bridson,Conder and Reid.Hence the triangle groups are distinguished among themselves by their finite quotients.We focus on the question about quantifying the size of a quotient which separates two triangle groups and give an explicit upper bound.
文摘For any pair of orientable closed hyperbolic 3-manifolds,this paper shows that any isomorphism between the profinite completions of their fundamental groups witnesses a bijective correspondence between the Zariski dense PSL(2,Q^(ac))-representations of their fundamental groups,up to conjugacy;moreover,corresponding pairs of representations have identical invariant trace fields and isomorphic invariant quaternion algebras.(Here,Q^(ac)denotes an algebraic closure of Q.)Next,assuming the p-adic Borel regulator injectivity conjecture for number fields,this paper shows that uniform lattices in PSL(2,C)with isomorphic profinite completions have identical invariant trace fields,isomorphic invariant quaternion algebras,identical covolume,and identical arithmeticity.
基金supported by the National Natural Science Foundation of China (No. 11925101)the National Key R&D Program of China (No. 2020YFA0712800)。
文摘Surface bundles arising from periodic mapping classes may sometimes have non-isomorphic, but profinitely isomorphic fundamental groups. Pairs of this kind have been discovered by Hempel. This paper exhibits examples of nontrivial Hempel pairs where the mapping tori can be distinguished by some Turaev-Viro invariants, and also examples where they cannot be distinguished by any Turaev-Viro invariants.
基金supported(in part)by the research funds of Chonbuk National University
文摘Let X and Y be connected nilpotent CW-complexes of finite type. In this paper we deal with another complete analysis of a set of phantom maps in terms of strong homology by using the derived functors. We also prove that the set of homotopy classes of maps is independent of the choice of both rational homotopy equivalent classes and completion genera.
