实射影空间上的有理环空间

射影平面的有理类似

Rational analogs of projective planes

本文研究了高维闭光滑流形的存在性，它的有理同伦类型类似于射影平面。应用理性手术，该问题可以归结为寻找满足Hirzebruch签名公式和一组同余关系的可能庞特里亚金数，这相当于寻找丢番图方程的解。

有理多面体与具有序单位的射影格序阿贝尔群

Rational polyhedra and projective lattice-ordered abelian groups with order unit

l-群G是具有平移不变格序的阿贝尔群。Baker和Beynon证明了G是n-生成的射影当且仅当它是n-表示的.一个单位l-群是一个具有特殊阶单位的l-群G，即，G中的元素u，其正整数倍数最终支配G中的每个元素。当每个n-生成的射影单位l-群都被n-表示时，一般情况下，其逆命题不成立。本文将经典代数拓扑学（a la Whitehead）与环面簇的弱Oda猜想的Wododarczyk-Morelli解相结合，来描述环生成的单位l-群.

四元数射影空间的圈同调

Loop homology of quaternionic projective spaces

确定了四元数射影空间和八元数射影平面的整圈同调的Batalin-Vilkovisky代数结构.

同调型的等效射影空间和格拉斯曼流形的有理稳定性类型

Rational stable homotopy type of equivariant projective spaces and Grassmannians

本文研究了等效复射影空间和格拉斯曼流形在复表示下的有理稳定性类型，通过显式分裂展示了其结构特征。

Rational homotopy of complex projective varieties with normal isolated singularities

Let X be a complex projective variety of dimension n with only isolated normal singularities. In this paper we prove, using mixed Hodge theory, that if the link of each singular point of X is (n-2)-connected, then X is a formal topological space. This result applies to a large class of examples, such as normal surface singularities, varieties with ordinary multiple points, hypersurfaces with isolated singularities and more generally, complete intersections with isolated singularities. We obtain analogous results for contractions of subvarieties.

Loop homological invariants associated to real projective spaces

Let A be a based subspace of Y. Under the assumptions that Y is path-connected and that the reduced diagonal map of A induces the zero map in all mod 2 reduced homology groups, we compute a formula for the mod 2 reduced Poincaré series of the loop space $Ω((A \wedge \mathbb{RP}^\infty) \cup_{A \wedge \mathbb{RP}^1} (Y \wedge \mathbb{RP}^1))$. Here $\mathbb{RP}^\infty$ and $\mathbb{RP}^1$ denote the infinite real projective space and the real projective line respectively.