Exotic 4-manifolds with signature zero
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910415364030464 |
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| author | Baykur, R. Inanc Hamada, Noriyuki |
| author_facet | Baykur, R. Inanc Hamada, Noriyuki |
| contents | We produce infinitely many distinct irreducible smooth 4-manifolds homeomorphic to #(2m+1)(CP^2 # -CP^2) and #(2n+1)(S^2 x S^2), respectively, for each m>3 and n>4. These provide the smallest exotic closed simply connected 4-manifolds with signature zero known to date, and in each one of these homeomorphism classes, we get minimal symplectic 4-manifolds. Our novel exotic 4-manifolds are derived from fairly special small Lefschetz fibrations we build via positive factorizations in the mapping class group, with spin and non-spin monodromies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10908 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exotic 4-manifolds with signature zero Baykur, R. Inanc Hamada, Noriyuki Geometric Topology Differential Geometry Symplectic Geometry We produce infinitely many distinct irreducible smooth 4-manifolds homeomorphic to #(2m+1)(CP^2 # -CP^2) and #(2n+1)(S^2 x S^2), respectively, for each m>3 and n>4. These provide the smallest exotic closed simply connected 4-manifolds with signature zero known to date, and in each one of these homeomorphism classes, we get minimal symplectic 4-manifolds. Our novel exotic 4-manifolds are derived from fairly special small Lefschetz fibrations we build via positive factorizations in the mapping class group, with spin and non-spin monodromies. |
| title | Exotic 4-manifolds with signature zero |
| topic | Geometric Topology Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2305.10908 |