Perfect discrete Morse functions on Stratifoldds

Abstract

In this paper, we study the computation of optimal discrete Morse functions on stratifolds. In particular, we present an algorithm that efficiently computes such functions for a broad class of them. Moreover, we characterize the conditions under which these functions are perfect.

Figures (6)

• Figure 1: Left: Geometric representation of a discrete vector field $V$. Right: Morse matching of the same discrete vector field $V$. The pairs belonging to $V$ are marked in blue.
• Figure 2: CW structure of the spaces in $\mathcal{M}$ after identifications.
• Figure 3: CW structure of a stratifold $X_1$ with $\mathcal{M} = \{\mathbb{T}^2 \# \mathbb{T}^2, \mathbb{T}^2 \# \mathbb{T}^2, \mathbb{R}P^2\}$.
• Figure 4: Graph associated with the stratifold $X_1$ shown in \ref{['fig:strat']}.
• Figure 5: Result of applying the algorithm to a triangulation of the space $S(\mathbb{S}^2, (1, 1))$.

Theorems & Definitions (28)

• Theorem 2.1
• Theorem 2.2
• Theorem 2.3
• proof
• Theorem 2.4
• Theorem 2.5
• Theorem 2.6
• Theorem 2.7
• Theorem 3.1
• proof