2018/04/17 by Juhnke-Kubitzke, Martina, Venturello, Lorenzo
#Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1804.06270
A classical result by Pachner states that two d-dimensional combinatorial manifolds with boundary are PL homeomorphic if and only they can be connected by a sequence of shellings and inverse shellings. We prove that for balanced, i.e., properly (d + 1)-colored, manifolds such a sequence can be chosen such that balancedness is preserved in each step. As a key ingredient we establish that any two balanced PL homeomorphic combinatorial manifolds with the same boundary are connected by a sequence of basic cross-flips, as was shown recently by Izmestiev, Klee and Novik for balanced manifolds without boundary. Moreover, we enumerate combinatorially different basic cross-flips and show that roughly half of these suffice to relate any two PL homeomorphic manifolds.