The non-orientable 4-genus of a knot [Formula: see text] in [Formula: see text] is defined to be the minimum first Betti number of a non-orientable surface [Formula: see text] smoothly embedded in [Formula: see text] so that [Formula: see text] bounds [Formula: see text]. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots. We will also view obstructions to a knot bounding a Möbius band given by the double branched cover of [Formula: see text] branched over [Formula: see text].
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Slope of orderable Dehn filling of two-bridge knots
In this paper, we study the Riley polynomial of double twist knots with higher genus. Using the root of the Riley polynomial, we compute the range of rational slope [Formula: see text] such that [Formula: see text]-filling of the knot complement has left-orderable fundamental group. Further more, we make a conjecture about left-orderable surgery slopes of two-bridge knots.
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- Award ID(s):
- 1811156
- PAR ID:
- 10413383
- Date Published:
- Journal Name:
- Journal of Knot Theory and Its Ramifications
- Volume:
- 31
- Issue:
- 01
- ISSN:
- 0218-2165
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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