Let $\unicode[STIX]{x1D6E4}$ denote the mapping class group of the plane minus a Cantor set. We show that every action of $\unicode[STIX]{x1D6E4}$ on the circle is either trivial or semiconjugate to a unique minimal action on the so-called simple circle.

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Given a finite subgroup G G of the mapping class group of a surface S S , the Nielsen realization problem asks whether G G can be realized as a finite group of homeomorphisms of S S . In 1983, Kerckhoff showed that for S S a finite-type surface, any finite subgroup G G may be realized as a group of isometries of some hyperbolic metric on S S . We extend Kerckhoff’s result to orientable, infinite-type surfaces. As applications, we classify torsion elements in the mapping class group of the plane minus a Cantor set, and also show that topological groups containing sequences of torsion elements limiting to the identity do not embed continuously into the mapping class group of S S . Finally, we show that compact subgroups of the mapping class group of S S are finite, and locally compact subgroups are discrete.

National standards for natural resources (NSNR) plays an important role in promoting efficient use of China's natural resources, which sets standards for many domains such as marine and land resources. Its revision is difficult since standards in different domains may overlap or conflict. To facilitate the revision of NSNR, this paper extracts structural knowledge from the NSNR files to assist its revision. NSNR files are in multi-domain texts, where the traditional knowledge extraction methods could fall short in recalling multi-domain entities. To address this issue, this paper proposes a knowledge extraction method for multi-domain texts, including sub-domain relation discovery (SRD) and domain semantic features fusion (DSFF) module. SRD splits NSNR into sub-domains to facilitate the relation discovery. DSFF integrates relation features in the conditional random field (CRF) model to improve the capability of multi-domain entity recognition. Experimental results demonstrate that the proposed method could effectively extract structural knowledge from NSNR.

Let S S be a surface and let Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) be the mapping class group of S S permuting a Cantor subset K ⊂ S K \subset S . We prove two structure theorems for normal subgroups of Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) . (Purity:) if S S has finite type, every normal subgroup of Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) either contains the kernel of the forgetful map to the mapping class group of S S , or it is ‘pure’ — i.e. it fixes the Cantor set pointwise. (Inertia:) for any n n element subset Q Q of the Cantor set, there is a forgetful map from the pure subgroup PMod ⁡ ( S , K ) \operatorname {PMod}(S,K) of Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) to the mapping class group of ( S , Q ) (S,Q) fixing Q Q pointwise. If N N is a normal subgroup of Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) contained in PMod ⁡ ( S , K ) \operatorname {PMod}(S,K) , its image N Q N_Q is likewise normal. We characterize exactly which finite-type normal subgroups N Q N_Q arise this way. Several applications and numerous examples are also given.