论文标题
在iWase的歧管上
On Iwase's manifolds
论文作者
论文摘要
在〜\ cite {iw2} iwase中构建了两个16维流形的$ m_2 $和$ m_3 $，其中ls-category 3是Ganea的猜想的反例：$ {\ rm cat_ {lm cat_ {ls}}（m \ times s^n）= 1 = {\ rm cat_ $+rm rm cat_} M.我们表明，歧管$ m_3 $是歧管正方形的对数定律的反示例：$ {\ rm cat_ {ls {ls}}}（m \ times m）= 2 {\ rm cat_ {ls cat_ {ls}}} m $。另外，我们构建了一张$$ f：n \ to m_2 \ times m_3 $$的学位地图，这将Rudyak的猜想减少到问题上是否$ {\ rm cat_ {ls {ls}}（M_2 \ times m_3）\ ge 5 $。我们表明$ {\ rm cat_ {ls}}（m_2 \ times m_3）\ ge 4 $。
In ~\cite{Iw2} Iwase has constructed two 16-dimensional manifolds $M_2$ and $M_3$ with LS-category 3 which are counter-examples to Ganea's conjecture: ${\rm cat_{LS}} (M\times S^n)={\rm cat_{LS}} M+1$. We show that the manifold $M_3$ is a counter-example to the logarithmic law for the LS-category of the square of a manifold: ${\rm cat_{LS}}(M\times M)=2{\rm cat_{LS}} M$. Also, we construct a map of degree one $$f:N\to M_2\times M_3$$ which reduces Rudyak's conjecture to the question whether ${\rm cat_{LS}}(M_2\times M_3)\ge 5$. We show that ${\rm cat_{LS}}(M_2\times M_3)\ge 4$.
