|
|
某些曲线复形的连通性
|
Abstract:
在这篇文章中，我们给出了曲面和柄体上的四种单纯复形：non-equal complex，part cut system complex，non-equal disk complex，domain disk complex，并且研究了它们的连通性。
In this paper, we introduce non-equal complex, part cut system complex on the surface and non-equal disk complex, domain disk complex on the handlebody and study their connectivity.
| [1] | Harvey, W.J. (1981) Boundary Structure of the Modular Group. In: Kra, I. and Maskit, B., Eds., Riemann Surfacese and Related Topics (AM-97), Princeton University Press, 245-252. https://doi.org/10.1515/9781400881550-019 |
| [2] | Ivanov, N. (2001) Mapping Class Groups. In: Sher, R.B. and Daverman, R.J., Eds., Handbook of Geometric Topology, Elsevier, 523-633. https://doi.org/10.1016/b978-044482432-5/50013-5 |
| [3] | Farb, B. and Margalit, D. (2010) A Primer on Mapping Class Groups. Princeton University Press. |
| [4] | McCullough, D. (1991) Virtually Geometrically Finite Mapping Class Groups of 3-Manifolds. Journal of Differential Geometry, 33, 1-65. https://doi.org/10.4310/jdg/1214446029 |
| [5] | Scharlemann, M. (2003) Automorphisms of the 3-Sphere That Preserve a Genus Two Heegaard Splitting. arXiv: math/0307231. |
| [6] | Hatcher, A. and Thurston, W. (1980) A Presentation for the Mapping Class Group of a Closed Orientable Surface. Topology, 19, 221-237. https://doi.org/10.1016/0040-9383(80)90009-9 |
| [7] | Masur, H. and Schleimer, S. (2006) The Pants Complex Has Only One End. In: Minsky, Y.N., Sakuma, M. and Series, C., Eds., Spaces of Kleinian Groups, Cambridge University Press, 209-218. https://doi.org/10.1017/cbo9781139106993.010 |
| [8] | Harer, J.L. (1985) Stability of the Homology of the Mapping Class Groups of Orientable Surfaces. The Annals of Mathematics, 121, 215-249. https://doi.org/10.2307/1971172 |
| [9] | Wajnryb, B. (1998) Mapping Class Group of a Handlebody. Fundamenta Mathematicae, 158, 195-228. https://doi.org/10.4064/fm-158-3-195-228 |
| [10] | Guo, Q. and Liu, Q. (2016) Connectivity of Certain Simplicial Complexes Associated to a Handlebody. Journal of Knot Theory and Its Ramifications, 25, Article ID: 1650064. https://doi.org/10.1142/s0218216516500644 |
| [11] | Putman, A. (2006) A Note on the Connectivity of Certain Complexes Associated to Surfaces. arXiv: math/0612762. |
| [12] | 雷逢春. 三维流形组合拓扑基础[M]. 北京: 科学出版社, 2021. |
| [13] | Lickorish, W.B.R. (1964) A Finite Set of Generators for the Homeotopy Group of a 2-Manifold. Mathematical Proceedings of the Cambridge Philosophical Society, 60, 769-778. https://doi.org/10.1017/s030500410003824x |
| [14] | Takahashi, M. (1995) On the Generators of the Mapping Class Group of a $3$-Dimensional Handlebody. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 71, 213-214. https://doi.org/10.3792/pjaa.71.213 |
| [15] | McCarthy, J.D. and Papadopoulos, A. (2012) Simplicial Actions of Mapping Class Groups. In: Guichard, O., Ed., IRMA Lectures in Mathematics and Theoretical Physics, EMS Press, 297-423. https://doi.org/10.4171/103-1/6 |
