论文标题
有效的奇数托里
Efficient multisections of odd-dimensional tori
论文作者
论文摘要
鲁宾斯坦 - 蒂尔曼（Tillmann）通过定义pl $ n $ -manifolds的{\ it MultiSections}的3个manifolds和4个manifolds的Heegaard分裂概念，这些{\ it MultiSections}是分解为$ k = $ k = \ lfloor n/2 \ lfloor n/2 \ rfloor+1 $ $ $ n $ $ $ $ $ $ n $ -dimsents。对于每个奇数圆环$ t^n $，我们构造了一个多孔，它是{\ it有效}的意义上，因为每个1 handlebody都有属$ n $，我们证明这是最佳的；相对于索引上$ s_n $的排列操作和$ \ z_k $ translation Action沿主角对称性，每个多孔都是{\ it对称}。我们还构建了$ t^4 $的转移，将所有对称的Tori的对称多分子提升到某些立方体的歧管，并获得合并身份作为推论。
Rubinstein--Tillmann generalized the notions of Heegaard splittings of 3-manifolds and trisections of 4-manifolds by defining {\it multisections} of PL $n$-manifolds, which are decompositions into $k=\lfloor n/2\rfloor+1$ $n$-dimensional 1-handlebodies with nice intersection properties. For each odd-dimensional torus $T^n$, we construct a multisection which is {\it efficient} in the sense that each 1-handlebody has genus $n$, which we prove is optimal; each multisection is {\it symmetric} with respect to both the permutation action of $S_n$ on the indices and the $\Z_k$ translation action along the main diagonal. We also construct such a trisection of $T^4$, lift all symmetric multisections of tori to certain cubulated manifolds, and obtain combinatorial identities as corollaries.
