# Volume 23 (2019) No. 2

## Volume 23 (2019) No. 2

### Approximating diffeomorphisms by elements of Thompson’s groups $F$ and $T$

Deniz E. Stiegemann

**Abstract:**

We show how to approximate diffeomorphisms of the closed interval and the circle by elements of Thompson’s groups $F$ and $T$, respectively. This is relevant in the context of Jones’ continuum limit of discrete multipartite systems and its dynamics.

### A graph-theoretic viewpoint for discrete Morse theory

Teresa Hoekstra Mendoza

**Abstract:**

A well known theorem of discrete Morse theory states that a discrete vector field is acyclic if and only if it is a gradient vector field for a discrete Morse function $f$. In this paper we give a simple proof using a well known theorem in graph theory. We do the same for another well known result in discrete Morse theory that states that in a simplicial complex endowed with a discrete gradient vector field, if two critical cells of the same dimension are such that there exists a unique gradient path between them, we can find a new vector field for which these two cells are not critical and every other critical cell remains critical in the new field.

### Sequential motion planning in connected sums of real projective spaces

Jorge Aguilar-Guzmán Jesús González

**Abstract:**

In this short note we observe that the higher topological complexity of an iterated connected sum of real projective spaces is maximal possible. Unlike the case of regular TC, the result is accessible through easy mod 2 zero-divisor cup-length considerations.