著者

Charlton David Demaine Erik D. Demaine Martin L. Dujmovic Vida Morin Pat Uehara Ryuhei

出版者

World Scientific Publishing

雑誌

International Journal of Computational Geometry and Applications (ISSN:02181959)

巻号頁・発行日

vol.22, no.3, pp.207-214, 2012

---

A planar point set S is an (i, t) set of ghost chimneys if there exist lines H_0, H_1,…,H_<t-1> such that the orthogonal projection of S onto H_j consists of exactly i + j distinct points. We give upper and lower bounds on the maximum value of t in an (i, t) set of ghost chimneys, showing that it is linear in i.

著者

丹下 基生 TANGE MOTOO YAMADA YUICHI

出版者

World Scientific Publishing

雑誌

Journal of knot theory and its ramifications (ISSN:02182165)

巻号頁・発行日

vol.21, no.11, 2012-10

---

A framed knot with an integral coefficient determines a simply-connected 4-manifold by 2-handle attachment. Its boundary is a 3-manifold obtained by Dehn surgery along the framed knot. For a pair of such Dehn surgeries along distinct knots whose results are homeomorphic, it is a natural problem: Determine the closed 4-manifold obtained by pasting the 4-manifolds along their boundaries. We determine the complete list (set) of pairs of integral surgeries along distinct torus knots whose resulting manifolds are orientation preserving/reversing homeomorphic lens spaces, and study the closed 4-manifolds constructed as above. The list consists of five sequences. All framed links and Kirby calculus are indexed by integers. As a bi-product, some sequences of embeddings of lens spaces into the standard 4-manifolds are constructed.

著者

Charlton David Demaine Erik D. Demaine Martin L. Dujmovic Vida Morin Pat Uehara Ryuhei

出版者

World Scientific Publishing

雑誌

International Journal of Computational Geometry and Applications (ISSN:02181959)

巻号頁・発行日

vol.22, no.3, pp.207-214, 2012

---

A planar point set S is an (i, t) set of ghost chimneys if there exist lines H_0, H_1,…,H_<t-1> such that the orthogonal projection of S onto H_j consists of exactly i + j distinct points. We give upper and lower bounds on the maximum value of t in an (i, t) set of ghost chimneys, showing that it is linear in i.

著者

TANGE MOTOO YAMADA YUICHI

出版者

World Scientific Publishing

雑誌

Journal of knot theory and its ramifications (ISSN:02182165)

巻号頁・発行日

vol.21, no.11, pp.1250111, 2012-10

被引用文献数

3

---

A framed knot with an integral coefficient determines a simply-connected 4-manifold by 2-handle attachment. Its boundary is a 3-manifold obtained by Dehn surgery along the framed knot. For a pair of such Dehn surgeries along distinct knots whose results are homeomorphic, it is a natural problem: Determine the closed 4-manifold obtained by pasting the 4-manifolds along their boundaries. We determine the complete list (set) of pairs of integral surgeries along distinct torus knots whose resulting manifolds are orientation preserving/reversing homeomorphic lens spaces, and study the closed 4-manifolds constructed as above. The list consists of five sequences. All framed links and Kirby calculus are indexed by integers. As a bi-product, some sequences of embeddings of lens spaces into the standard 4-manifolds are constructed.