Corpus ID: 237491642

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

Figures from this paper

References

SHOWING 1-10 OF 16 REFERENCES
On Simply-Connected 4-Manifolds
This paper concerns (but does not succeed in performing) the diffeomorphism classification of closed, oriented, differential, simply-connected 4-manifolds. It arises out of the observation (due toExpand
The Genus of Embedded Surfaces in the Projective Plane
1. Statement of the result The genus of a smooth algebraic curve of degree d in CP is given by the formula g = (d − 1)(d − 2)/2. A conjecture sometimes attributed to Thom states that the genus of theExpand
A note on the complexity of h–cobordisms
We show that the number of double points of smoothly immersed 2-spheres representing certain homology classes of an oriented, smooth, closed, simply-connected 4-manifold X must increase with theExpand
Topology of 4-manifolds
One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topologicalExpand
Smooth Four-Manifolds and Complex Surfaces
This book applies the recent techniques of gauge theory to study the smooth classification of compact complex surfaces. The study is divided into four main areas: Classical complex surface theory,Expand
Periodicity of branched cyclic covers
Let K C S 2n+1 be a simple fibered knot, that is, an embedding of an (n -2 ) connected (2n-1)-manifold K in the (2n+ 1)-sphere whose complement fibers over S x with ( n 1)-connected fibers. (See 1.5Expand
MONOPOLE EQUATION AND THE 11 8-CONJECTURE
Note that if the intersection form of M is definite, a theorem of S.K. Donaldson implies b2(M) = sign(M) = 0 ([6,7]). V. A. Rohlin’s theorem implies that k = − sign(M)/16 is an integer ([15]). Let b+Expand
On the topological 4-genus of torus knots
We prove that the topological locally flat slice genus of large torus knots takes up less than three quarters of the ordinary genus. As an application, we derive the best possible linear estimate ofExpand
Immersions of manifolds.
  • R. Cohen
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1982
This paper outlines a proof of the conjecture that every compact, differentiable, n-dimensional manifold immerses in Euclidean space of dimension 2n - alpha(n), where alpha(n) is the number of onesExpand
Connections
In the year that Britain's railways were actually linked to the Continental European systems, the author uses his own personal experience to examine how co-operation within the developing industryExpand
...
1
2
...