# On the Thom conjecture in $CP^3$

@inproceedings{Ruberman2021OnTT, title={On the Thom conjecture in \$CP^3\$}, author={Daniel Ruberman and Marko Slapar and Savso Strle}, year={2021} }

What is the simplest smooth simply connected 4-manifold embedded in CP homologous to a degree d hypersurface Vd? A version of this question associated with Thom asks if Vd has the smallest b2 among all such manifolds. While this is true for degree at most 4, we show that for all d ≥ 5, there is a manifold Md in this homology class with b2(Md) < b2(Vd). This contrasts with the Kronheimer-Mrowka solution of the Thom conjecture about surfaces in CP, and is similar to results of Freedman for 2n… Expand

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