7 problems

Let $K$ be a knot, let $\sg(K)$ denote its signature, let $D=\dt(K)$ be the determinant, let $H_1$ denote the first homology group of the double branched cover of $K$, and let…

Kim–Livingston's conjecture. If $M$ is algebraically nullbordant, then $M$ is nullbordant in $\widehat{\Theta}_3^\mathbb{Q}$.

Let $N$ be a closed connected orientable $n$-manifold with $H_1(N)$ torsion-free, $n\geq 4$, and $n$ even, and let $N_0$ denote a punctured version of $N$. For an embedding…

The paper studies embeddings of punctured $n$-manifolds $N_0$ in $\mathbb{R}^{2n-1}$ and associates to each embedding $f$ a Seifert linking form $L(f)$, an integer-valued symmetric…

Kim–Livingston conjecture. This homomorphism is an isomorphism.

Let $\widehat{\Theta}^3_{\mathbf Q}$ denote the topological cobordism group of rational homology three-spheres, and let $W(\mathbf Q/\mathbf Z)$ be the Witt group of nonsingular…

Let $X_0$ be an isolated hypersurface singularity with link $L=X_0\cap S$, and suppose $n=2m+2$. The non-vanishing cohomology groups of $L$ are … For codimension $m$ cycles $A$ and…