Probing topological relation between high density and low density region
  of 2MASS with hexagon cells
  We introduce a new 2-D hexagon technique to probe the topological structure
of the universe, in which we map regions of the sky with high and low galaxy
densities onto a 2-D lattice of hexagon unit cells, We define filled cells as
corresponding to high density regions and empty cells as corresponding to low
density region. The number of filled cells and empty cells are kept same by
controlling the size of the cells. By analyzing the six neighbors of each
hexagon we can get and compare statistical topological properties of the high
density and low density regions in the universe, in order to have a better
understanding of the evolution of the universe. We apply this hexagon method on
2MASS data and discover significant topological differences between the high
density and low density regions. Both regions have significant (>5 Sigma)
topological shifts from the binomial distribution or the random distribution.
