带系数群的内射性定理和代数闭包

Algebraic K-theory of group rings and the cyclotomic trace map

We prove that the Farrell-Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt-Schneider conjecture holds for cyclotomic fields. This generalizes a result of Bökstedt, Hsiang, and Madsen, and leads to a concrete description of a large direct summand of $K_n(\mathbb{Z}[G])\otimes_{\mathbb{Z}}\mathbb{Q}$ in terms of group homology. In many cases the number theoretic conjectures are true, so we obtain rational injectivity results about assembly maps, in particular fo…

T-齐次辫子的闭包是实代数的

Closures of T-homogeneous braids are real algebraic

本研究针对实代数链环的纤维化逆猜想，证明了一大类纤维化链环（含T-齐次辫子闭包等）是实代数的，构造了对应半全纯实多项式映射并给出次数信息。

Constructing links of isolated singularities of polynomials $\mathbb{R}^4\to\mathbb{R}^2$

We show that if a braid $B$ can be parametrised in a certain way, then previous work can be extended to a construction of a polynomial $f:\mathbb{R}^4\to\mathbb{R}^2$ with the closure of $B$ as the link of an isolated singularity of $f$, showing that the closure of $B$ is real algebraic. In particular, we prove that closures of squares of strictly homogeneous braids and certain lemniscate links are real algebraic. We also show that the constructed polynomials satisfy the strong Milnor condition, providing an explicit fibration of the complement of the closure of $B$ over $S^1$.

几何群的代数K-理论

Algebraic K-theory of Geometric Groups

本文通过同伦理论技术证明几何有限群的K-理论组装映射等价，并展示了该结果在群同调和几何中的应用。

Deroin-Tholozan表示的映射类群轨道闭包

Mapping class group orbit closures for Deroin-Tholozan representations

研究Deroin-Tholozan表示的特征簇中映射类群轨道的稠密性，利用辛结构证明作用的最小性。