论文标题
曲折的空间和简单歧管上的面部枚举
Toric spaces and face enumeration on simplicial manifolds
论文作者
论文摘要
在本文中，我们以拓扑方式研究了合理同源性领域的众所周知$ g $概念。为此，我们构建了一类具有圆环动作的拓扑空间，可以将其视为曲折品种的拓扑概括。沿着这种方式，我们证明，在任意合理同源性领域的某个中维面上进行出色的细分操作后，$ g $ conconture是有效的。此外，我们提供了有关Buchsbaum复合物和简单歧管的几个基本代数结果的拓扑证明。在此过程中，我们还将在复曲面拓扑中获得一些有趣的结果。
In this paper, we study the well-know $g$-conjecture for rational homology spheres in a topological way. To do this, we construct a class of topological spaces with torus actions, which can be viewed as topological generalizations of toric varieties. Along this way we prove that after doing stellar subdivision operations at some middle dimensional faces of an arbitrary rational homology sphere, the $g$-conjecture is valid. Furthermore, we give topological proofs of several fundamental algebraic results about Buchsbaum complexes and simplicial manifolds. In this process, we also get a few interesting results in toric topology.
