Constructing infinitely many smooth structures on small 4‐manifolds
By Anar Akhmedov, R. Baykur, B. Park. 2007
64 citations recorded by the source corpus.
The purpose of this article is two‐fold. First we outline a general construction scheme for producing simply connected minimal symplectic ‐manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain irreducible symplectic ‐manifolds homeomorphic but not diffeomorphic to ℂℙ2#(2k+1)ℂℙ¯2 for k = 1, …, 4, or to 3ℂℙ2#(2l+3)ℂℙ¯2 for l = 1, …, 6. Secondly, for each of these homeomorphism types, we show how to produce an infinite family of pairwise nondiffeomorphic nonsymplectic 4‐manifolds belonging to it. In particular, we prove that there are infinitely many exotic irreducible nonsymplectic smooth structures on, ℂℙ2#3ℂℙ¯2, 3ℂℙ2#5ℂℙ¯2 and 3ℂℙ2#7ℂℙ¯2 .
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d8d834fb9f28a0e5fc8749576e244fdf45f5d128
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Exotic smooth structures on small 4-manifolds with odd signatures (2007, methodology): “We can then compute the Seiberg-Witten invariants of X1(m) and check that infinitely many of them are distinct by applying exactly the same argument as in [3, 10] using the product formulas in [20].”