曲面上（Z_p^k）^m方向保持作用的分类

对于保幂操作的复杂定向，p-典型性是非典型的

For Complex Orientations Preserving Power Operations, p-typicality is Atypical

我们证明了，对于小于或等于13的素数p，许多著名的MU_（p）-环不允许交换MU_（p）-代数的结构.这些光谱具有复杂的取向，通过布朗-彼得森光谱的因素，并对应于p-典型的形式群的法律。我们提供的计算表明，这样的因式分解是不兼容的复杂的协边的功率运算。这意味着，例如，如果E是Landweber正合MU_（p）-环，其相应的形式群律是正高度的p-典型的，则典范映射MU_（p）--> E不是H_ \infty环谱的映射.紧接着，BP、E（n）和E_n上的标准p-典型取向不能刚性化为E_ \infty环谱图。我们猜想类似的结果对所有素数都成立。

Homology and orientation reversing periodic maps on surfaces

In this paper, we give a classification of orientation reversing periodic maps on closed surfaces which generalizes the theory of Nielsen for the orientation preserving periodic maps. On one hand, we give a group of data for each orientation reversing periodic map such that two periodic maps with the same data must be conjugate to each other. On the other hand, we give the criterion to judge when two different groups of data correspond to the same conjugacy class. As an application of the results of this paper, we shall show that a given orientation reversing periodic map on $Σ_g$ with period …

Topological Symmetries of R^3

If a finite group acts topologically, faithfully and orientation preservingly on R^3, then it is isomorphic to a subgroup of SO(3).

$H{\Bbb C}P^3$的光滑自由对合及$S^3$嵌入$S^6$的Smith猜想

Smooth free involution of $H{\Bbb C}P^3$ and Smith conjecture for imbeddings of $S^3$ in $S^6$

本文建立了$H{\Bbb C}P^3$上自由对合的存在性与$S^6$上具有嵌入$S^3$的不动点集的对合的存在性之间的等价性，然后利用$H{\Bbb C}P^3$上的已知结果给出了$S^6$中嵌入$S^3$的Smith猜想的一族反例.此外，本文还证明了每个光滑同伦复射影3-空间不存在保向光滑自由对合，从而回答了一个公开问题[Pe]。此外，还研究了$H{\Bbb C}P^3$上光滑方向保持对合的存在性问题。

Reversing orientation homeomorphisms of surfaces

Let $M$ be a connected compact orientable surface, $f:M\to \mathbb{R}$ be a Morse function, and $h:M\to M$ be a diffeomorphism which preserves $f$ in the sense that $f\circ h = f$. We will show that if $h$ leaves invariant each regular component of each level set of $f$ and reverses its orientation, then $h^2$ is isotopic to the identity map of $M$ via $f$-preserving isotopy. This statement can be regarded as a foliated and a homotopy analogue of a well known observation that every reversing orientation orthogonal isomorphism of a plane has order $2$, i.e. is a mirror symmetry with respect to …