A characterization of the Murasugi polynomial of an equivariant slice knot

等变纽结与纽结Floer同调

Equivariant knots and knot Floer homology

本文使用纽结Floer同调定义了等变同痕不变量，给出了等变切片亏格下界并构造了强可逆切片纽结族，同时应用于检测切片圆盘奇异对及扩展稳定化距离结果。

等变切片强负手征结

Equivariantly slicing strongly negative amphichiral knots

本文利用行列式、Spinc-结构和Donaldson定理，证明了强负手征结在4-球中界定等变切片盘的障碍，并基于Heegaard Floer校正项给出了强负手征结的判定障碍。

Alexander polynomials of equivariant slice and ribbon knots in S^3

This paper gives an algebraic characterization of Alexander polynomials of equivariant ribbon knots and a factorization condition satisfied by Alexander polynomials of equivariant slice knots.

Deep and shallow slice knots in 4-manifolds

We consider slice disks for knots in the boundary of a smooth compact 4-manifold $X^{4}$. We call a knot $K \subset \partial X$ deep slice in $X$ if there is a smooth properly embedded 2-disk in $X$ with boundary $K$, but $K$ is not concordant to the unknot in a collar neighborhood $\partial X \times I$ of the boundary. We point out how this concept relates to various well-known conjectures and give some criteria for the nonexistence of such deep slice knots. Then we show, using the Wall self-intersection invariant and a result of Rohlin, that every 4-manifold consisting of just one 0- and a n…

关于源自$\u2124_2$-等变Seiberg–Witten Floer上同调的切片环面不变量$q_M$

On the slice-torus invariant $q_M$ from $\mathbb{Z}_2$-equivariant Seiberg--Witten Floer cohomology

该数学研究证明Iida–Taniguchi提出的$\u2124$-值切片环面不变量$q_M$无法由多种已知的纽结配边不变量线性组合表示，明确了该不变量的独立性。

强可逆纽结的等变代数协边性

Equivariant algebraic concordance of strongly invertible knots

该研究通过不变Seifert曲面定义新的等变代数协边群及同态Φ，证明其提升已有等变同态与符号，给出群同构型部分结果、新的等变片纽结障碍与片亏格下界，还可阻碍Alexander多项式为1的纽结的等变片纽结性。

Khovanov 同调与等变曲面

Khovanov homology and equivariant surfaces

本文通过精细化 Bar-Natan 同调构造新数值不变量，证明强可逆纽结的等变切片亏格与同痕等变切片亏格之差可任意大。

等变奇异瞬子Floer理论中的无定向辫正合三角形

Unoriented skein exact triangles in equivariant singular instanton Floer theory

本文将等变奇异瞬子Floer理论从纽结扩展到非零行列式链环，证明了无定向辫正合三角形，实现了Murasugi符号行为的范畴化，并揭示了L-space纽结与瞬子范畴化的潜在联系。

对合Khovanov同调与等变纽结II

Involutive Khovanov homology and equivariant knots II

本文将对合Khovanov同调框架推广到对合缠结，实现了相关同调与不变量的分治加速计算，并得到存在奇异切片圆盘对的强可逆纽结新例子。

Equivariant extension properties of coset spaces of locally compact groups and approximate slices

We prove that for a compact subgroup $H$ of a locally compact Hausdorff group $G$, the following properties are mutually equivalent: (1) $G/H$ is a manifold, (2) $G/H$ is finite-dimensional and locally connected, (3) $G/H$ is locally contractible, (4) $G/H$ is an ANE for paracompact spaces, (5) $G/H$ is a metrizable $G$-ANE for paracompact proper $G$-spaces having a paracompact orbit space. A new version of the Approximate slice theorem is also proven in the light of these results.

8字结的(2,1)-缆线结不是光滑切片

The $(2,1)$-cable of the figure-eight knot is not smoothly slice

本文通过证明8字结的(2,1)-缆线结的分支双覆盖不界定等变同调球，从而证明该缆线结不是光滑切片。

切片群胚的等变上同调

Equivariant cohomology of slice groupoids

本文通过构造Weil或Cartan模型之间的自然链映射，证明了切片邻域的等变上同调与切片上的等变上同调同构，并引入切片群胚概念，推广等变理论至此类群胚，证明等变上同调在Morita等价下不变。

等变配边的一个新不变量与2-桥结的相关结果

A new invariant of equivariant concordance and results on 2-bridge knots

该研究聚焦2-桥结的等变配边类，给出蝶形多项式计算公式、证明无等变切片2-桥结，还提出强可逆结的新等变配边不变量，借此证明2-桥结等变配边阶为无穷。

奇异圆盘与奇异瞬子Floer同调

Exotic disks and singular instanton Floer homology

利用带Chern-Simons滤波的奇异瞬子Floer同调构造奇异切片圆盘对，并证明存在强可逆Z-切片纽结，其任意对称Z-圆盘对均为奇异且稳定后仍奇异。

involutive Khovanov homology 和 equivariant knots

Involutive Khovanov homology and equivariant knots

本文提出了一种involutive Khovanov同调，用于研究强不可约结的exotic slice disks性质，并重新证明了Hayden的无限族结J_n的exotic性。

周期2结在S⁴中的等变同伦群

Equivariant concordance of periodic 2-knots in $S^4$

研究显示，在S⁴中周期2结的等变光滑同伦群与非等变情况不同，本文提出新的不变量并证明其分类结果。

A counterexample to the strong version of Freedman's conjecture

A long-standing conjecture due to Michael Freedman asserts that the 4-dimensional topological surgery conjecture fails for non-abelian free groups, or equivalently that a family of canonical examples of links (the generalized Borromean rings) are not A-B slice. A stronger version of the conjecture, that the Borromean rings are not even weakly A-B slice, where one drops the equivariant aspect of the problem, has been the main focus in search for an obstruction to surgery. We show that the Borromean rings, and more generally all links with trivial linking numbers, are in fact weakly A-B slice. T…

解结数、带状协边与奇异瞬子

Unknotting number, ribbon concordance, and singular instantons

利用等变奇异瞬子弗洛尔理论，研究通过带状协边得到的切片纽结的解结操作，发现同号解结序列需含两种符号，还给出三维流形类似情况，为德恩手术数单调性提供证据。

来自Seiberg-Witten理论的纽结同痕不变量与4-流形中的切片亏格下界

Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds

本文利用等变Seiberg-Witten-Floer上同调构造了一族新的纽结同痕不变量 $θ^{(q)}(K)$，并证明它们能给出定4-流形中同调平凡光滑曲面的亏格下界，推广了 $ν^+(K)$ 的相关结果。

陈-西蒙斯泛函、奇异瞬子与四维 clasp 数

Chern-Simons functional, singular instantons, and the four-dimensional clasp number

本文利用源自等变奇异瞬子理论并与陈-西蒙斯泛函相关的纽结不变量，肯定回答了四维 clasp 数与切片亏格之差可否任意大的问题，同时解决 Livingston 猜想，并研究奇异瞬子 Frøyshov 不变量及其在无向切片亏格、环面纽结表示和协边中的应用。

负 amphichiral 纽结与半 Conway 多项式

Negative amphichiral knots and the half-Conway polynomial

本文定义并研究强负 amphichiral 纽结的半 Conway 多项式，建立等变 skein 计算方法与解结数下界，完整刻画可实现多项式，并构造行列式为1的非 slice 新例子。

Brieskorn 球面、循环群作用与 Milnor 猜想

Brieskorn spheres, cyclic group actions and the Milnor conjecture

本文发展了等变 Seiberg-Witten-Floer 上同调理论，应用于 Brieskorn 同调球面：给出了 Milnor 猜想的新证明，并证明了特定群作用无法光滑延拓到以该球面为边界的可缩光滑 4-流形上。