2016/02/10 by Rubinstein, J. Hyam, Tillmann, Stephan
#52B70 #53C21 #57N15 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1602.03279
Recently Gay and Kirby described a new decomposition of smooth closed 4-manifolds called a trisection. This paper generalises Heegaard splittings of 3-manifolds and trisections of 4-manifolds to all dimensions, using triangulations as a key tool. In particular, we prove that every closed piecewise linear n-manifold has a multisection, i.e. can be divided into k+1 n-dimensional 1-handlebodies, where n=2k+1 or n=2k, such that intersections of the handlebodies have spines of small dimensions. Several applications, constructions and generalisations of our approach are given.