• 대한수학회지
• /
• 제52권6호
• /
• pp.1305-1321
• /
• 2015

We dene new link invariants which are called the quasitoric braid index and the cyclic length of a link and show that the quasitoric braid index of link with k components is the product of k and the cycle length of link. Also, we give bounds of Gordian distance between the (p,q)-torus knot and the closure of a braid of two specific quasitoric braids which are called an alternating quasitoric braid and a blockwise alternating quasitoric braid. We give a method of modication which makes a quasitoric presentation from its braid presentation for a knot with braid index 3. By using a quasitoric presentation of $10_{139}$ and $10_{124}$, we can prove that $u(10_{139})=4$ and $d^{\times}(10_{124},K(3,13))=8$.

• Kyungpook Mathematical Journal
• /
• 제55권1호
• /
• pp.191-203
• /
• 2015

We introduce a quasitoric virtual braid and show that every virtual link can be obtained by the closure of a quasitoric virtual braid. Also, we show that the set of quasitoric virtual braids with n strands forms a group which is a subgroup of the n-virtual braid group.

• 대한수학회지
• /
• 제54권3호
• /
• pp.733-748
• /
• 2017

We give Hodge structures on quasitoric orbifolds. We define orbifold Hodge numbers and show a correspondence of orbifold Hodge numbers for crepant resolutions of quasitoric orbifolds. In short we extend Hodge structures to a non almost complex setting.

• 대한수학회보
• /
• 제49권4호
• /
• pp.761-765
• /
• 2012

We prove that for a toric manifold (respectively, a quasitoric manifold) M, any graded ring isomorphism $H^*(M){\rightarrow}H^*({\Pi}_{i=1}^{m}\mathbb{C}P^{ni})$ can be realized by a diffeomorphism (respectively, a homeomorphism) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.

• 대한수학회보
• /
• 제59권3호
• /
• pp.671-683
• /
• 2022

The aim of this paper is to deal with the realization problem of a given Lagrangian submanifold of a symplectic manifold as the fixed point set of an anti-symplectic involution. To be more precise, let (X, ω, µ) be a toric Hamiltonian T-space, and let ∆ = µ(X) denote the moment polytope. Let τ be an anti-symplectic involution of X such that τ maps the fibers of µ to (possibly different) fibers of µ, and let p₀ be a point in the interior of ∆. If the toric fiber µ^-1(p₀) is real Lagrangian with respect to τ, then we show that p₀ should be the origin and, furthermore, ∆ should be centrally symmetric.