# Tight complexes in 3-space admit perfect discrete Morse functions

## Karim Adiprasito, Bruno Benedetti – 2012

Focus Area 3: Topological connectivity and diameter of Discrete Structures In 1967, Chillingworth proved that all convex simplicial 3-balls are collapsible. Using the classical notion of tightness, we generalize this to arbitrary manifolds: We show that all tight simplicial 3-manifolds admit some perfect discrete Morse function. We also strengthen Chillingworth's theorem by proving that all convex simplicial 3-balls are non-evasive. In contrast, we show that many non-evasive 3-balls are not convex.

Title

Tight complexes in 3-space admit perfect discrete Morse functions

Author

Karim Adiprasito, Bruno Benedetti

Date

2012-02

Source(s)

Type

Text

Size or Duration

13 pages