对合赫戈弗洛尔同调中的自然性与函子性

实Heegaard Floer理论中的自然性

Naturality in real Heegaard Floer theory

本文证明了实Heegaard Floer同调、实纽结Floer同调及实缝合Floer同调的自然性，还定义了对合实Heegaard Floer同调，补充了相关理论性质。

On naturality of the Ozsvath-Szabo contact invariant

We discuss functoriality properties of the Ozsvath-Szabo contact invariant, and expose a number of results which seemed destined for folklore. We clarify the (in)dependence of the invariant on the basepoint, prove that it is functorial with respect to contactomorphisms, and show that it is strongly functorial under Stein cobordisms.

Heegaard Floer同调中的射影自然性

Projective Naturality in Heegaard Floer Homology

该研究在Heegaard Floer同调领域，证明了Heegaard Floer不变量可给出到$\text{Mod}_{\text{Mod}}$射影化范畴中可迁系统范畴的函子，揭示了其底层射影同伦范畴结构，并给出对合同调应用及推广方向。

A transverse knot invariant from Z2-equivariant Heegaard Floer cohomology

We define an invariant of based transverse links, as a well-defined element inside the equivariant Heegaard Floer cohomology of its branched double cover, defined by Lipschitz, Hendricks, and Sarkar. We prove the naturality and functoriality of equivariant Heegaard Floer cohomology for branched double covers of $S^3$ along based knots, and then prove that our transverse link invariant $c_{\mathbb{Z}_{2}}(ξ_{K})$ is an well-defined element which is always nonvanishing and functorial under certain classes of symplectic cobordisms, and describe its behavior under negative stabilization. It follow…

Heegaard Floer 理论中的典范定向

Canonical orientations in Heegaard Floer theory

本文在整数环上建立 Heegaard Floer 理论，利用典范定向证明其自然性，并给出手术正合三角的新证明及对合 Heegaard Floer 同调的定义。

Lipshitz–Ozsváth–Thurston对应关系的不变分裂原理

Invariant splitting principles for the Lipshitz--Ozsváth--Thurston correspondence

该研究证明Lipshitz-Ozsváth-Thurston对应关系的不变分裂原理，给出从伴随纽结对合Floer同调计算卫星同调的新方法，还构造了无限多个一次稳定化后仍奇异的可缩4-流形对。