Back to Search
Start Over
Representing 3-manifolds in the complex number plane.
- Source :
-
Topology & Its Applications . Oct2017, Vol. 230, p425-443. 19p. - Publication Year :
- 2017
-
Abstract
- A complete invariant defined for (closed, connected, orientable) 3-manifolds is an invariant defined for the 3-manifolds such that any two 3-manifolds with the same invariant are homeomorphic. Further, if the 3-manifold itself is reconstructed from the data of the complete invariant, then it is called a characteristic invariant defined for the 3-manifolds. In previous papers by the first author, a characteristic lattice point invariant and a characteristic rational invariant defined for the 3-manifolds were constructed which also produced a smooth real function with the definition interval ( − 1 , 1 ) as a characteristic invariant defined for the 3-manifolds. In this paper, a complex number-valued characteristic invariant for the 3-manifolds whose norm is smaller than or equal to one half is introduced by using an embedding of a set of lattice points called the ADelta set, distinct from the PDelta set, into the set of complex numbers. The distributive situation for the invariants of the 3-manifolds of lengths up to 10 is plotted in the complex number plane with radius smaller than or equal to one half. By using this complex number-valued characteristic invariant, a holomorphic function with the unit open disk as the definition domain which is called the characteristic quantity function is constructed as a characteristic invariant defined for the 3-manifolds. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01668641
- Volume :
- 230
- Database :
- Academic Search Index
- Journal :
- Topology & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 125233107
- Full Text :
- https://doi.org/10.1016/j.topol.2017.08.036