Topological symmetry groups and mapping class groups for spatial graphs

Abstract

The first-named author is supported in part by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (2012R1A1A1006520). The second-named author is supported in part by Grant-in-Aid for Young Scientists (B) (no. 20525167), Japan Society for the Promotion of Science.The authors wish to express their gratitude to Erica Flapan for posing the question and to Darryl McCullough for providing his very helpful idea on the topic. Part of this work was carried out while the second-named author was visiting the Mathematisches Forschungsinstitut Oberwolfach. The institute kindly offered these accommodations when his university was affected by the 2011 Tohoku earthquake. He is grateful to the MFO and its staff for the offer, financial support, and their warm hospitality. He would also like to thank the Leibniz Association for travel support. Finally, the authors are grateful to an anonymous referee whose helpful comments improved the presentation.