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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Representing characteristic homology classes of $m\mathbf {C}\mathrm {P}^2 \# n\mathbf {\overline {C}}\mathrm {P}^2$
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by Jian Han Guo and Dan Yan Gan PDF
Proc. Amer. Math. Soc. 121 (1994), 1251-1255 Request permission

Abstract:

We prove the following theorems. Theorem 1. If $m,n \geq 1,x \in {H_2}(mC{P^2}\# n{\overline {CP} ^2})$ is a characteristic homology class with ${x^2} = 16l + m - n > 0$ and (1) $m < 3l + 1$ provided $l \geq 0$, or (2) $m < - 19l + 1$ provided $l < 0$. Suppose that the 11/8-conjecture is true. Then x cannot be represented by a smoothly embedded 2-sphere. Theorem 2. Let $m,n \geq 4l > 0,x \in {H_2}(mC{P^2}\# n{\overline {CP} ^2})$ be a primitive characteristic homology class with ${x^2} = \pm 16l + m - n$. Then x can be represented by a smoothly embedded 2-sphere.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 1251-1255
  • MSC: Primary 57R95; Secondary 57R40
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1205494-7
  • MathSciNet review: 1205494