Abstract
The twin group
Funding statement: Mahender Singh is supported by the Swarna Jayanti Fellowship grants DST/SJF/MSA-02/2018-19 and SB/SJF/2019-20/04.
Acknowledgements
The authors are grateful to Valeriy Bardakov for his interest in this work and for his many useful comments. Tushar Kanta Naik and Neha Nanda thank IISER Mohali for the Post Doctoral and the PhD Research Fellowships, respectively.
References
[1] V. Bardakov, M. Singh and A. Vesnin, Structural aspects of twin and pure twin groups, Geom. Dedicata 203 (2019), 135–154. 10.1007/s10711-019-00429-1Suche in Google Scholar
[2] A. Bartholomew, R. Fenn, N. Kamada and S. Kamada, Doodles on surfaces, J. Knot Theory Ramifications 27 (2018), no. 12, Article ID 1850071. 10.1142/S0218216518500712Suche in Google Scholar
[3] A. Bartholomew, R. Fenn, N. Kamada and S. Kamada, Colorings and doubled colorings of virtual doodles, Topology Appl. 264 (2019), 290–299. 10.1016/j.topol.2019.06.028Suche in Google Scholar
[4] R. Fenn and P. Taylor, Introducing doodles, Topology of Low-dimensional Manifolds (Chelwood Gate 1977), Lecture Notes in Math. 722, Springer, Berlin (1979), 37–43. 10.1007/BFb0063187Suche in Google Scholar
[5] A. Genevois, Contracting isometries of CAT(0) cube complexes and acylindrical hyperbolicity of diagram groups, Algebr. Geom. Topol. 20 (2020), no. 1, 49–134. 10.2140/agt.2020.20.49Suche in Google Scholar
[6] J. González, J. L. León-Medina and C. Roque, Linear motion planning with controlled collisions and pure planar braids, preprint (2019), https://arxiv.org/abs/1902.06190v2. 10.4310/HHA.2021.v23.n1.a15Suche in Google Scholar
[7] K. Gotin, Markov theorem for doodles on two-sphere, preprint (2018), https://arxiv.org/abs/1807.05337. Suche in Google Scholar
[8] V. Guba and M. Sapir, Diagram groups, Mem. Amer. Math. Soc. 620 (1997), 1–117. 10.1090/memo/0620Suche in Google Scholar
[9] N. L. Harshman and A. C. Knapp, Anyons from three-body hard-core interactions in one dimension, Ann. Physics 412 (2020), Article ID 168003. 10.1016/j.aop.2019.168003Suche in Google Scholar
[10] L. D. James, Complexes and Coxeter groups—operations and outer automorphisms, J. Algebra 113 (1988), no. 2, 339–345. 10.1016/0021-8693(88)90163-9Suche in Google Scholar
[11] A. Kaul and M. E. White, Centralizers of Coxeter elements and inner automorphisms of right-angled Coxeter groups, Int. J. Algebra 3 (2009), no. 9–12, 465–473. Suche in Google Scholar
[12] M. Khovanov, Doodle groups, Trans. Amer. Math. Soc. 349 (1997), no. 6, 2297–2315. 10.1090/S0002-9947-97-01706-6Suche in Google Scholar
[13] R. S. Kulkarni, Dynamical types and conjugacy classes of centralizers in groups, J. Ramanujan Math. Soc. 22 (2007), no. 1, 35–56. Suche in Google Scholar
[14] R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Classics Math., Springer, Berlin, 2001. 10.1007/978-3-642-61896-3Suche in Google Scholar
[15] J. Mostovoy and C. Roque-Márquez, Planar pure braids on six strands, J. Knot Theory Ramifications 29 (2020), no. 1, Article ID 1950097. 10.1142/S0218216519500974Suche in Google Scholar
[16] B. Mühlherr, Automorphisms of graph-universal Coxeter groups, J. Algebra 200 (1998), no. 2, 629–649. 10.1006/jabr.1997.7230Suche in Google Scholar
[17] M. V. Neshchadim, Inner automorphisms and some of their generalizations, Sib. Èlektron. Mat. Izv. 13 (2016), 1383–1400. Suche in Google Scholar
[18] K. H. Rosen, J. G. Michaels, J. L. Gross, J. W. Grossman and D. R. Shier, Handbook of Discrete and Combinatorial Mathematics, CRC Press, Boca Raton, 2000. 10.1201/9781439832905Suche in Google Scholar
[19] G. B. Shabat and V. A. Voevodsky, Drawing curves over number fields, The Grothendieck Festschrift. Vol. III, Progr. Math. 88, Birkhäuser, Boston (1990), 199–227. 10.1007/978-0-8176-4576-2_8Suche in Google Scholar
[20] J. Tits, Sur le groupe des automorphismes de certains groupes de Coxeter, J. Algebra 113 (1988), no. 2, 346–357. 10.1016/0021-8693(88)90164-0Suche in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Conjugacy classes and automorphisms of twin groups
- Decomposition and classification of length functions
- Successive coefficients of close-to-convex functions
- Frobenius cowreaths and Morita contexts
- The non-linear sewing lemma III: Stability and generic properties
- On hyperquadrics containing projective varieties
- Explicit Burgess-like subconvex bounds for GL2 × GL1
- Characterisation of polyhedral products with finite generalised Postnikov decomposition
- Solvable Lie and Leibniz superalgebras with a given nilradical
- Alvis–Curtis duality for representations of reductive groups with Frobenius maps
- The third partial cohomology group and existence of extensions of semilattices of groups by groups
- Instanton bundles on two Fano threefolds of index 1
- Carleson measure characterizations of the Campanato type space associated with Schrödinger operators on stratified Lie groups
Artikel in diesem Heft
- Frontmatter
- Conjugacy classes and automorphisms of twin groups
- Decomposition and classification of length functions
- Successive coefficients of close-to-convex functions
- Frobenius cowreaths and Morita contexts
- The non-linear sewing lemma III: Stability and generic properties
- On hyperquadrics containing projective varieties
- Explicit Burgess-like subconvex bounds for GL2 × GL1
- Characterisation of polyhedral products with finite generalised Postnikov decomposition
- Solvable Lie and Leibniz superalgebras with a given nilradical
- Alvis–Curtis duality for representations of reductive groups with Frobenius maps
- The third partial cohomology group and existence of extensions of semilattices of groups by groups
- Instanton bundles on two Fano threefolds of index 1
- Carleson measure characterizations of the Campanato type space associated with Schrödinger operators on stratified Lie groups