{"product_id":"invariants-and-pictures-low-dimensional-topology-and-combinatorial-group-theory-hardcover","title":"Invariants and Pictures: Low-Dimensional Topology and Combinatorial Group Theory - Hardcover","description":"\u003cp\u003eby \u003cb\u003eVassily Olegovich Manturov\u003c\/b\u003e (Author), \u003cb\u003eDenis Fedoseev\u003c\/b\u003e (Author), \u003cb\u003eSeongjeong Kim\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of \u003cem\u003eG\u003csub\u003en\u003c\/sub\u003e\u003csup\u003ek\u003c\/sup\u003e\u003c\/em\u003e groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.\u003c\/p\u003e\u003cp\u003eIn 2015, V O Manturov defined a two-parametric family of groups \u003cem\u003eG\u003csub\u003en\u003c\/sub\u003e\u003csup\u003ek\u003c\/sup\u003e\u003c\/em\u003e and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in \u003cem\u003eG\u003csub\u003en\u003c\/sub\u003e\u003csup\u003ek\u003c\/sup\u003e\u003c\/em\u003e.\u003c\/p\u003e\u003cp\u003eThe book is devoted to various realisations and generalisations of this principle in the broad sense. The groups \u003cem\u003eG\u003csub\u003en\u003c\/sub\u003e\u003csup\u003ek\u003c\/sup\u003e\u003c\/em\u003e have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups -- \u003cem\u003eΓ\u003csub\u003en\u003c\/sub\u003e\u003csup\u003ek\u003c\/sup\u003e\u003c\/em\u003e, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 388\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.88 x 9 x 6 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e April 16, 2020\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":47466385801394,"sku":"9789811220111","price":191.16,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0770\/3891\/1666\/files\/e44a343b4843c8e0e4065ce7c86a01df.webp?v=1779020458","url":"https:\/\/box.dadyminds.org\/products\/invariants-and-pictures-low-dimensional-topology-and-combinatorial-group-theory-hardcover","provider":"DADYMINDS BOX","version":"1.0","type":"link"}