2000 character limit reached
On four-manifolds without 1- and 3-handles
Published 21 Mar 2024 in math.GT | (2403.14586v1)
Abstract: We note that infinitely many irreducible, closed, simply connected 4-manifolds, with prescribed signature and spin type, admit perfect Morse functions, i.e. they can be given handle decompositions without 1- and 3-handles. In particular, there are many such 4-manifolds homeomorphic but not diffeomorphic to the standard 4-manifolds # m (S2 x S2) and # n (CP2 # -CP2), respectively, which answers Problem 4.91 on Kirby's 1997 list.
- R. I. Baykur. Minimality and fiber sum decompositions of Lefschetz fibrations. Proc. Amer. Math. Soc., 144(5):2275–2284, 2016. doi:10.1090/proc/12835.
- R. I. Baykur and N. Hamada. Lefschetz fibrations with arbitrary signature, 2020. to appear: J. Eur. Math. Soc. arXiv:2010.11916.
- R. I. Baykur and N. Hamada. Exotic 4-manifolds with signature zero, 2023. arXiv:2305.10908.
- H. Endo. Meyer’s signature cocycle and hyperelliptic fibrations. Math. Ann., 316(2):237–257, 2000. doi:10.1007/s002080050012.
- M. J. D. Hamilton and D. Kotschick. Minimality and irreducibility of symplectic four-manifolds. Int. Math. Res. Not., pages Art. ID 35032, 13, 2006. doi:10.1155/IMRN/2006/35032.
- R. Kirby. Problems in low–dimensional topology. In W. Kazez, editor, Geometric Topology. American Math. Soc./International Press, Providence, 1997.
- I. Smith. Lefschetz fibrations and the Hodge bundle. Geom. Topol., 3:211–233, 1999. doi:10.2140/gt.1999.3.211.
- M. Usher. Minimality and symplectic sums. Int. Math. Res. Not., pages Art. ID 49857, 17, 2006. doi:10.1155/IMRN/2006/49857.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.