{"product_id":"9781470468705-dehn-fillings-of-knot-manifolds-con","title":"Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eWe show that if a hyperbolic knot manifold M contains an essential twice-punctured torus F with boundary slope ? and admits a filling with slope ? producing a Seifert fibred space, then the distance between the slopes ? and ? is less than or equal to 5 unless M is the exterior of the figure eight knot.\u003cbr\u003eWe show that if a hyperbolic knot manifold M contains an essential twicepunctured torus F with boundary slope ? and admits a filling with slope ? producing a Seifert fibred space, then the distance between the slopes ? and ? is less than or equal to 5 unless M is the exterior of the figure eight knot. The result is sharp; the bound of 5 can be realized on infinitely many hyperbolic knot manifolds. We also determine distance bounds in the case that the fundamental group of the ?-filling contains no non-abelian free group. The proofs are divided into the four cases F is a semi-fibre, F is a fibre, F is non-separating but not a fibre, and F is separating but not a semi-fibre, and we obtain refined bounds in each case.\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":54845454025078,"sku":"9781470468705","price":68.38,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_36047039_04ba8741-686b-49ca-8a52-a88e55b9d3c3.jpg?v=1757580523","url":"https:\/\/www.rarewaves.com\/products\/9781470468705-dehn-fillings-of-knot-manifolds-con","provider":"Rarewaves.com","version":"1.0","type":"link"}