English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We prove the following theorems.  Theorem 1.   If       m , n ≥  1 , x ∈  H 2 ( m C P 2 #  n C P ¯  2 ) m,n \geq 1,x \in {H_2}(mC{P^2}\# n{\overline {CP} ^2})        is a characteristic homology class with       x 2 = 16 l + m −  n &gt; 0 {x^2} = 16l + m - n &gt; 0        and  (1)      m &gt; 3 l + 1 m &gt; 3l + 1        provided       l ≥  0 l \geq 0      ,  or  (2)      m &gt; −  19 l + 1 m &gt; - 19l + 1        provided       l &gt; 0 l &gt; 0      .  Suppose that the 11/8-conjecture is true. Then x cannot be represented by a smoothly embedded 2-sphere .  Theorem 2.   Let       m , n ≥  4 l &gt; 0 , x ∈  H 2 ( m C P 2 #  n C P ¯  2 ) m,n \geq 4l &gt; 0,x \in {H_2}(mC{P^2}\# n{\overline {CP} ^2})        be a primitive characteristic homology class with       x 2 = ±  16 l + m −  n {x^2} = \pm 16l + m - n      .  Then x can be represented by a smoothly embedded 2-sphere .

Representing characteristic homology classes of 𝑚𝐂𝐏²#𝐧\overline{𝐂}𝐏²