과제정보
연구 과제 주관 기관 : National Research Foundation(NRF) of Korea
참고문헌
- M. F. Atiyah, The signature of fibre-bundles, Global Analysis (Papers in Honor of K. Kodaira), pp. 73-84, Univ. Tokyo Press, Tokyo, 1969.
- R. I. Baykur and D. Margalit, Indecomposable surface bundles over surfaces, J. Topol. Anal. 5 (2013), no. 1, 161-181. https://doi.org/10.1142/S179352531350009X
- K. S. Brown, Cohomology of Groups, Graduate Texts in Mathematics 87, Springer-Verlag, 1982.
- J. Bryan and R. Donagi, Surface bundles over surfaces of small genus, Geom. Topol. 6 (2002), 59-67. https://doi.org/10.2140/gt.2002.6.59
- J. Bryan, R. Donagi, and A. Stipsicz, Surface bundles: some interesting examples, Turkish J. Math. 25 (2001), no. 1, 61-68.
- H. Endo, A construction of surface bundles over surfaces with non-zero signature, Osaka J. Math. 35 (1998), no. 4, 915-930.
- H. Endo, Meyer's signature cocycle and hyperelliptic fibrations, Math. Ann. 316 (2000), no. 2, 237-257. https://doi.org/10.1007/s002080050012
- H. Endo, M. Korkmaz, D. Kotschick, B. Ozbagci, and A. Stipsicz, Commutators, Lefschetz fibrations and the signatures of surface bundles, Topology 41 (2002), no. 5, 961-977. https://doi.org/10.1016/S0040-9383(01)00011-8
- H. Endo, T. E. Mark, and J. Van Horn-Morris, Monodromy substitutions and rational blowdowns, J. Topol. 4 (2011), no. 1, 227-253. https://doi.org/10.1112/jtopol/jtq041
- H. Endo and S. Nagami Signature of relations in mapping class groups and nonholomorphic Lefschetz fibrations, Trans. Amer. Math. Soc. 357 (2005), no. 8, 3179-3199. https://doi.org/10.1090/S0002-9947-04-03643-8
- B. Farb and D. Margalit, A primer on mapping class groups, Princeton Mathematical Series 49 Princeton University Press, Princeton, NJ, 2012.
- N. Hamada, Upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus, Michigan Math. J. 63 (2014), no. 2, 275-291. https://doi.org/10.1307/mmj/1401973051
- U. Hamenstadt, Signatures of Surface bundles and Milnor Wood Inequalities, preprint, http://arxiv.org/pdf/1206.0263
- J. Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math. 72 (1983), no. 2, 221-239. https://doi.org/10.1007/BF01389321
- F. Hirzebruch, The signature of ramified coverings, Global Analysis (Papers in Honor of K. Kodaira), pp. 253-265, Univ. Tokyo Press, Tokyo, 1969.
- M. Hoster, A new proof of the signature formula for surface bundles, Topology Appl. 112 (2001), no. 2, 205-213. https://doi.org/10.1016/S0166-8641(99)00233-3
- R. Kirby, Problems in Low-Dimensional Topology, in W. Kazez(Ed.), Geometric Topology, AMS/IP Studies in Advanced Mathematics, Vol.2.2, American Mathematical Society, Providence, RI, 1997.
- K. Kodaira, A certain type of irregular algebraic surfaces, J. Anal. Math. 19 (1967), 207-215.
- M. Korkmaz, Stable Commutator Length of a Dehn Twist, Michigan Math. J. 52 (2004), no. 1, 23-31. https://doi.org/10.1307/mmj/1080837732
- M. Korkmaz and B. Ozbagci, Minimal number of singular fibers in a Lefschetz fibration, Proc. Amer. Math. Soc. 129 (2001), no. 5, 1545-1549. https://doi.org/10.1090/S0002-9939-00-05676-8
- M. Korkmaz and B. Ozbagci, On sections of elliptic fibrations, Michigan Math. J. 56 (2008), no. 1, 77-87. https://doi.org/10.1307/mmj/1213972398
- M. Korkmaz and A. Stipsicz, The second homology groups of mapping class groups of oriented surfaces, Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 3, 479-489. https://doi.org/10.1017/S0305004102006461
- D. Kotschick, Signatures, Monopoles, and Mapping class groups, Math. Res. Lett. 5 (1998), no. 1-2, 227-234. https://doi.org/10.4310/MRL.1998.v5.n2.a9
- Y. Matsumoto, Lefschetz Fibrations of genus two - a topological approach, Topology and Teichmuller spaces, 123-148, World Sci.Publ., River Edge, NJ, 1996.
- W. Meyer, Die Signatur von lokalen Koeffzientensystemen und Faserbundeln, Bonn. Math. Schr. 53 (1972), 59 pp.
- W. Meyer, Die Signatur von Flachenbundeln, Math. Ann. 201 (1973), 239-264. https://doi.org/10.1007/BF01427946
- S. Morita, Characteristic classes of surface bundles, Invent. Math. 90 (1987), no. 3, 551-577. https://doi.org/10.1007/BF01389178
- B. Ozbagci, Signatures of Lefschetz fibrations, Pacific J. Math. 202 (2002) no. 1, 99-118.
- J. Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978), no. 3, 347-350. https://doi.org/10.1090/S0002-9939-1978-0494115-8
- T. Sakasai, Lagrangian mapping class groups from a group homological point of view, Algebr. Geom. Topol. 12 (2012), no. 1, 267-291. https://doi.org/10.2140/agt.2012.12.267
- A. Stipsicz, Surface bundles with nonvanishing signature, Acta Math. Hungar. 95 (2002), no. 4, 299-307. https://doi.org/10.1023/A:1015649208611
- B. Wajnryb, An elementary approach to the mapping class group of a surface, Geom. Topol. 3 (1999), 405-466. https://doi.org/10.2140/gt.1999.3.405
- C. T. C. Wall, Non-additivity of the signature, Invent. Math. 7 (1969), 269-274. https://doi.org/10.1007/BF01404310