## Nihonkai Mathematical Journal

- Nihonkai Math. J.
- Volume 26, Number 1 (2015), 37-45.

### The configuration space of a model for $5$-membered straight-chain hydrocarbon molecules parametrized by chain lengths

Satoru Goto, Kazushi Komatsu, and Jun Yagi

#### Abstract

We provide a mathematical model of $n$-membered straight-chain hydrocarbon molecules. The configuration space of the model is parametrized by chain lengths. By assuming the bond angle conditions required for hydrocarbon molecules, we determine the topological types of fibers of the configuration space of the model by chain lengths when $n = 5$.

#### Article information

**Source**

Nihonkai Math. J., Volume 26, Number 1 (2015), 37-45.

**Dates**

First available in Project Euclid: 30 March 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.nihmj/1459343069

**Mathematical Reviews number (MathSciNet)**

MR3482756

**Zentralblatt MATH identifier**

1338.92149

**Subjects**

Primary: 52C99: None of the above, but in this section

Secondary: 57M50: Geometric structures on low-dimensional manifolds 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 92E10: Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

**Keywords**

Configuration space molecular structure

#### Citation

Goto, Satoru; Komatsu, Kazushi; Yagi, Jun. The configuration space of a model for $5$-membered straight-chain hydrocarbon molecules parametrized by chain lengths. Nihonkai Math. J. 26 (2015), no. 1, 37--45. https://projecteuclid.org/euclid.nihmj/1459343069