A presentation for the mapping class group of the closed non-orientable surface of genus 4

In [B. Szepietowski, A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves, Osaka J. Math. 45 (2008) 283–326] we proposed a method of finding a finite presentation for the mapping class group of a non-orientable surface by using its action on the so called ordered complex of curves. In this paper we use this method to obtain an explicit finite presentation for the mapping class group of the closed non-orientable surface of genus 4. The set of generators in this presentation consists of 5 Dehn twists, 3 crosscap transpositions and one involution, and it can be immediately reduced to the generating set found by Chillingworth [D.R.J. Chillingworth, A finite set of generators for the homeotopy group of a non-orientable surface, Proc. Camb. Phil. Soc. 65 (1969) 409–430].