Back to Search
Start Over
Four-dimensional manifolds constructed by lens space surgeries of distinct types.
- Source :
- Journal of Knot Theory & Its Ramifications; Oct2017, Vol. 26 Issue 11, p-1, 51p
- Publication Year :
- 2017
-
Abstract
- 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 study pairs of lens space surgeries along distinct knots whose lens spaces (i.e. the resulting lens spaces of the surgeries) are orientation-preservingly or -reversingly homeomorphic. In the authors' previous work, we treated with the case both knots are torus knots. In this paper, we focus on the case where one is a torus knot and the other is a Berge's knot Type VII or VIII, in a genus one fiber surface. We determine the complete list (set) of such pairs of lens space surgeries and study the closed 4-manifolds constructed as above. The list consists of six sequences. All framed links and handle calculus are indexed by integers. [ABSTRACT FROM AUTHOR]
- Subjects :
- MANIFOLDS (Mathematics)
KNOT theory
INTEGRALS
HOMEOMORPHISMS
INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 26
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 125559372
- Full Text :
- https://doi.org/10.1142/S0218216517500699