2-亏格为2的三维流形的对称变换

有限Coxeter群的强对称亏格

The strong symmetric genus of the finite Coxeter groups

有限群G的强对称亏格是可定向闭拓扑曲面的最小亏格，在该曲面上G忠实地充当一组定向保持自同构。本文完成了除E_8群以外的所有有限Coxeter群的强对称亏格的计算。

Classification of Groups with Strong Symmetric Genus up to Twenty-Five

The strong symmetric genus of a finite group is the minimum genus of a compact Riemann surface on which the group acts as a group of automorphisms preserving orientation. A characterization of the infinite number of groups with strong symmetric genus zero and one is well-known and the problem is finite for each strong symmetric genus greater than or equal to two. May and Zimmerman have published papers detailing the classification of all groups with strong symmetric genus two through four. Using the computer algebra system GAP, we extend these classifications to all groups of strong symmetric …

超八面体群的强对称亏格

The strong symmetric genus of the hyperoctahedral groups

群的强对称亏格是曲面的最小曲面的亏格，在曲面上，群忠实地充当方向保持自同构群。本文给出并证明了超八面体群的强对称亏格。这个参数是已知的交替和对称群以及零星有限单群。

等变双切环面、稳定化与等变稳定化

Equivariant Double-Slice Genus, Stabilization, and Equivariant Stabilization

本文研究了强可逆结的等变双切环面和超切环面，通过下界证明发现了一类具有特定性质的结，并探讨了其在稳定化距离中的应用。

Signature, positive Hopf plumbing and the Coxeter transformation

By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations are positive real or lie on the unit circle. By optimally bounding the signature of tree-like positive Hopf plumbings from below by the genus, we prove that at least two thirds of them lie on the unit circle. In contrast, we show that for divide links, the signature cannot be linearly bounded from below by the genus.

Some Centrally Symmetric Manifolds

We show existence of centrally symmetric maps on surfaces all of whose faces are quadrangles and pentagons for each orientable genus $g \geq 0$. We also show existence of centrally symmetric maps on surfaces all of whose faces are hexagons for each orientable genus $g = 2k-1$, $k\in \mathbb{N}$. We enumerate centrally symmetric triangulated manifolds of dimensions 2 and 3 with few vertices.