{"product_id":"the-quadratic-isoperimetric-inequality-for-mapping-tori-of-free-group-automorphisms","title":"The Quadratic Isoperimetric Inequality for Mapping Tori of Free Group Automorphisms","description":"\u003cp\u003eThe authors prove that if $F$ is a finitely generated free group and $\\phi$ is an automorphism of $F$ then $F\\rtimes_\\phi\\mathbb Z$ satisfies a quadratic isoperimetric inequality. The authors' proof of this theorem rests on a direct study of the geometry of van Kampen diagrams over the natural presentations of free-by-cylic groups. The main focus of this study is on the dynamics of the time flow of $t$-corridors, where $t$ is the generator of the $\\mathbb Z$ factor in $F\\rtimes_\\phi\\mathbb Z$ and a $t$-corridor is a chain of 2-cells extending across a van Kampen diagram with adjacent 2-cells abutting along an edge labelled $t$. The authors prove that the length of $t$-corridors in any least-area diagram is bounded by a constant times the perimeter of the diagram, where the constant depends only on $\\phi$. The authors' proof that such a constant exists involves a detailed analysis of the ways in which the length of a word $w\\in F$ can grow and shrink as one replaces $w$ by a sequence of words $w_m$, where $w_m$ is obtained from $\\phi(w_{m-1})$ by various cancellation processes. In order to make this analysis feasible, the authors develop a refinement of the improved relative train track technology due to Bestvina, Feighn and Handel.\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003eAuthor:\u003c\/b\u003e Martin R. Bridson, Daniel Groves\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublisher:\u003c\/b\u003e American Mathematical Soc.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublished:\u003c\/b\u003e 2010-01-15\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePages:\u003c\/b\u003e 170\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Soc.","offers":[{"title":"Default Title","offer_id":62806770647411,"sku":"9780821846315","price":200.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0987\/0812\/8115\/files\/content_93a2b56f-29f7-45b1-9d73-240610175de9.jpg?v=1777888885","url":"https:\/\/readaura.store\/products\/the-quadratic-isoperimetric-inequality-for-mapping-tori-of-free-group-automorphisms","provider":"Read Aura","version":"1.0","type":"link"}