A note on the complexity of h–cobordisms

Schwartz, Hannah

doi:10.2140/agt.2020.20.3313

Cited by 2 publications

(1 citation statement)

References 36 publications

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“…This condition can be satisfied since double points of either sign may be added locally to Σ 1 i by replacing a disk with the trace of a homotopy of arcs in R 3 obtained by the sequence of a first Reidemeister move, followed by a crossing change and another first Reidemeister move. (See [13,Figure 2] for a picture of this process.) We may further assume that the regular homotopy is in general position, so it is a sequence of isotopies, finger moves and Whitney moves [5, §1.6].…”

Section: Ambient Surgerymentioning

confidence: 99%

On the Thom conjecture in $CP^3$

Ruberman,

Slapar,

Strle

2021

Preprint

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What is the simplest smooth simply connected 4-manifold embedded in CP 3 homologous to a degree d hypersurface V d ? A version of this question associated with Thom asks if V d has the smallest b 2 among all such manifolds. While this is true for degree at most 4, we show that for all d ≥ 5, there is a manifoldThis contrasts with the Kronheimer-Mrowka solution of the Thom conjecture about surfaces in CP 2 , and is similar to results of Freedman for 2n-manifolds in CP n+1 with n odd and greater than 1.

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Section: Ambient Surgerymentioning

confidence: 99%

On the Thom conjecture in $CP^3$

Ruberman,

Slapar,

Strle

2021

Preprint

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On the Thom Conjecture in ℂℙ3

Ruberman

Slapar

Strle

2021

International Mathematics Research Notices

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What is the simplest smooth simply connected $4$-manifold embedded in $\mathbb {C}\mathbb {P}^3$ homologous to a degree $d$ hypersurface $V_d$? A version of this question associated with Thom asks if $V_d$ has the smallest $b_2$ among all such manifolds. While this is true for degree at most $4$, we show that for all $d \geq 5$, there is a manifold $M_d$ in this homology class with $b_2(M_d) < b_2(V_d)$. This contrasts with the Kronheimer–Mrowka solution of the Thom conjecture about surfaces in $\mathbb {C}\mathbb {P}^2$ and is similar to results of Freedman for $2n$-manifolds in $\mathbb {C}\mathbb {P}^{n+1}$ with $n$ odd and greater than $1$.

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A note on the complexity of h–cobordisms

Cited by 2 publications

References 36 publications

On the Thom conjecture in $CP^3$

On the Thom conjecture in $CP^3$

On the Thom Conjecture in ℂℙ3

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