## View abstract

### Session S28 - Knots, Surfaces, 3-manifolds

Wednesday, July 14, 18:00 ~ 18:30 UTC-3

## On classification of genus $g$ knots which admit a $(1,1)$-decomposition

### Fabiola Manjarrez-Gutiérrez

#### UNAM, México   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak4673c75b9a4cd94751d8a017b647b838').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy4673c75b9a4cd94751d8a017b647b838 = 'f&#97;b&#105;&#111;l&#97;.m&#97;nj&#97;rr&#101;z' + '&#64;'; addy4673c75b9a4cd94751d8a017b647b838 = addy4673c75b9a4cd94751d8a017b647b838 + '&#105;m' + '&#46;' + '&#117;n&#97;m' + '&#46;' + 'mx'; var addy_text4673c75b9a4cd94751d8a017b647b838 = 'f&#97;b&#105;&#111;l&#97;.m&#97;nj&#97;rr&#101;z' + '&#64;' + '&#105;m' + '&#46;' + '&#117;n&#97;m' + '&#46;' + 'mx';document.getElementById('cloak4673c75b9a4cd94751d8a017b647b838').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy4673c75b9a4cd94751d8a017b647b838 + '\'>'+addy_text4673c75b9a4cd94751d8a017b647b838+'<\/a>';

Given an oriented minimal genus Seifert surface $F'$ for a $(1,1)$-knot $K$ it is possible to surger $F'$ along annuli to obtain a simple minimal Seifert surface $F$. Such a surface can be put in a very nice position with respect to the $(1,1)$-position of the knot $K$. Using this kind of surfaces we give a description of a $(1,1)$-knot of genus $g$ as a vertical banding of $(1,1)$-knots of genus smaller than $g$. In addition, we show that any rational knot of genus $g$ is obtained as a vertical banding of $g$ genus one rational knots.

Joint work with Mario Eudave-Muñoz (UNAM) and Enrique Ramírez-Losada (CIMAT).