Concatenation of two oriented curves I've encountered a question with a notation I've never seen before, and I was wondering if I could get some clarification as to what it could mean. Here's an excerpt from the question:

Given two oriented curves $\mathbf{C}_1 : R_1(t) = (\sin t, \cos t, 0), 0 \leq t \leq \pi$ and $\mathbf{C}_2 : R_2(t) = (0, -\cos t, \sin t), 0 \leq t \leq \pi$, let $\mathbf{C}$ be the concatenation $\mathbf{C}_1 \cdot \mathbf{C}_2$.

Is the dot notation here ($\cdot$) effectively being used as a union ($\cup$) of the two curves? I noticed that the end points of the two curves match to form a loop, so I'm wondering if that's relevant here too.
Thank you!

What you noticed is exactly correct.
Here's the general definition of concatenation. Suppose that you have two parameterized curves of the form
$$c_1 : [0,a_1] \to \mathbb R^n, \qquad c_2 : [0,a_2] \to \mathbb R^n
$$
Suppose also that $c_1(a_1)=c_2(0)$, so the terminal endpoint of curve $c_1$ is the same as the initial endpoint of curve $c_2$. The concatenation of $c_1$ with $c_2$, which I will denote $c_1 * c_2$ instead of re-using that over-used "dot" notation, is the curve
$$c_1 * c_2 : [0,a_1 + a_2] \to \mathbb R^n
$$
defined by
$$c_1 * c_2(t) = \begin{cases}
c_1(t) &\quad\text{if $0 \le t \le t_1$} \\
c_2(t-a_1) &\quad\text{if $t_1 \le t \le t_1 + t_2$}
\end{cases}
$$
One thing that's nice about this notation is that you can then use it in path integral settings, and you get equations like this:
$$\int_{c_1 * c_2} \text{[something]} \, dt = \int_{c_1} \text{[something]}\, dt + \int_{c_2} \text{[something]}\, dt
$$
I'll mention also that this concatenation notation becomes very important in more advanced courses, particularly topology.
