Homotopy invariants of Gauss phrases A. Gibson 57M9968R15Gauss phrasesnanophraseshomotopy invariant Equivalence relations can be defined on Gauss phrases using combinatorial moves. In this paper we consider two closely related equivalence relations on Gauss phrases, homotopy and open homotopy. In particular, in each case, we define a new invariant and determine the values that it can attain. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3850 10.1512/iumj.2010.59.3850 en Indiana Univ. Math. J. 59 (2010) 207 - 230 state-of-the-art mathematics http://iumj.org/access/