Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those ...
Natural Dowling analogues of the complex of phylogenetic trees are studied. Using discrete Morse theory, we find their homotopy types. In the process, the homotopy types of certai...
In [1] it was developed o-minimal homotopy for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we also extend these res...
Numerical homotopy continuation gives a powerful tool for the applied scientist who seeks solutions to a system of polynomial equations. Techniques from numerical homotopy continu...