On spatial theta-curves with the same
-fold and
-fold branched covering
Abstract
In this note, we study two types of spatial theta-curves having two
-knotswhose each has two
-knotsand a trivial knot or two trivial knots and a
-bridge knot as constituent knots. Weshow that there is a
-manifold
such that
is the
-fold and
-fold covering of
branched over each type of spatial theta-curve. Furthermore, weinvestigate certain relations between the spatial theta-curves and between the closed
-manifolds which are coverings of
branched over them.
![(1,1)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/fb0ce7c2864d45cd277575f863f6af1c.png)
![(1,1)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/fb0ce7c2864d45cd277575f863f6af1c.png)
![2](http://siba-ese.unile.it/plugins/generic/latexRender/cache/c81e728d9d4c2f636f067f89cc14862c.png)
![3](http://siba-ese.unile.it/plugins/generic/latexRender/cache/eccbc87e4b5ce2fe28308fd9f2a7baf3.png)
![M](http://siba-ese.unile.it/plugins/generic/latexRender/cache/69691c7bdcc3ce6d5d8a1361f22d04ac.png)
![M](http://siba-ese.unile.it/plugins/generic/latexRender/cache/69691c7bdcc3ce6d5d8a1361f22d04ac.png)
![(Z_2\oplus Z_2)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/488b5cb65dd11815c9d49193ba028709.png)
![2](http://siba-ese.unile.it/plugins/generic/latexRender/cache/c81e728d9d4c2f636f067f89cc14862c.png)
![S^3](http://siba-ese.unile.it/plugins/generic/latexRender/cache/903faf99a14b55b7ad3d1020786c49a8.png)
![3](http://siba-ese.unile.it/plugins/generic/latexRender/cache/eccbc87e4b5ce2fe28308fd9f2a7baf3.png)
![S^3](http://siba-ese.unile.it/plugins/generic/latexRender/cache/903faf99a14b55b7ad3d1020786c49a8.png)
DOI Code:
10.1285/i15900932v23n1p111
Keywords:
Spatial theta-curve; Constituent knot; (1; 1)-knot
Classification:
57M12; 57M25
Full Text: PDF