arXiv subjects
Publications and source records attributed to Maki Nagura.
Let $M^{2n}$ be a closed smooth manifold homotopy equivalent to the complex projective space $\mathbb{C}P(n)$. The purpose of this paper is to show that when $n$ is even, the difference of the first Pontrjagin classes between $M^{2n}$ and $\mathbb{C}P(n)$ is divisible by 16.
In this paper, we introduce an equivalence relation on the set of local moves and classify local moves, called the extended $ST$-moves, up to the equivalence. Moreover, by inducing a binary relation on the set of equivalence classes of local moves, we show that an extended $ST$-move realizes the crossing change or the $SH(2)$-move. In addition, for any oriented knot and two extended $ST$-moves, we disscus the magnitude relation between the unknotting numbers of the knot via the moves, and show that there is an extended $ST$-move except $SH$-moves so that the knot can be transformed into the trivial knot by the single extended $ST$-move. Finally, we provide some examples of $ST$-moves with the binary relation.
We show some properties of a Seifert matrix of an $n$-component Brunnian link. In particular, we give a necessary and sufficient condition for a matrix to be a Seifert matrix of a 2-component Brunnian link up to S-equivalence.