{"paper":{"title":"Non-Reidemeister Knot Theory and Its Applications in Dynamical Systems, Geometry, and Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Vassily Olegovich Manturov","submitted_at":"2015-01-21T15:58:20Z","abstract_excerpt":"Classical knot theory deals with {\\em diagrams} and {\\em invariants}. By means of horizontal {\\em trisecants}, we construct a new theory of classical braids with invariants valued in {\\em pictures}.\n  These pictures are closely related to diagrams of the initial object.\n  The main tool is the notion of {\\em free $k$-braid group}. In the simplest case, for free $2$-braids, the word problem and the conjugacy problem can be solved by finding the minimal representative, which can be thought of as a graph, and is unique, as such.\n  We prove a general theorem about invariants of dynamical systems wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05208","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}