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* Gamefaqs (v. 1.3.1)As described in U.S. Pat. No. 5,487,944, the entire disclosure of which is incorporated herein by reference, an engine is a device that generates mechanical work through combustion of a fuel and an oxidant. The fuel and oxidant are premixed within a cylinder and ignition occurs to combust the mixture. The resulting combustion generates a force that is used to propel a piston in a reciprocal motion within the cylinder. The device can also be called a flame engine, combustion engine, reaction engine or chemical engine. The operative principle for the engine is not limited to reciprocating pistons and can be adapted to various non-reciprocal application, such as the spinning of turbines (e.g. propellers or windmills). The reaction engine can be used for some applications as engine; for other applications, the operation of the engine may be mechanically coupled to other apparatus such as a compressor, pump or turbine. Other types of reaction engines are used in systems such as rocket engines and spacecraft.
The manner in which the engine works is generally well known. For example, as described in U.S. Pat. No. 5,487,944, the entire disclosure of which is incorporated herein by reference, the engine includes a chamber containing a fuel which is ignited to sustain combustion and provide a force to move a piston within the chamber. The piston is coupled to a reaction device, such as a turbine, which converts the force generated by the piston into work (e.g. mechanical energy). Work is expressed as the product of the force applied to the piston and the distance the piston travels. The moving piston can be described as a reaction engine.
The reaction engine of U.S. Pat. No. 5,487,944 is referred to herein as a multi-chambered reaction engine. U.S. Pat. No. 5,487,944 teaches that a multi-chamber reaction engine may include a reaction cavity formed between a pair of cylinders. The reaction cavity of the multi-chambered reaction engine is flooded with fuel. The multi-chambered reaction engine generates a force to move a piston by igniting the fuel within the reaction cavity to sustain combustion, while simultaneously forcing the piston to reciprocate.
In the use of the multi-chambered reaction engine, it is contemplated that the engine may be used to power a vehicle, a

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Q:

Fundamental group of $X=D^2 \times I$

Let $D^2$ be a disc in the plane $\mathbb{R}^2$, and consider the space $X=D^2 \times I$. I want to find the fundamental group of it.
Clearly the fundamental group of $X \smallsetminus \partial X$ is the free group on two generators, since $X$ is obtained by attaching a single point $x \in S^2$ to $\Bbb{R}^2 \smallsetminus \{x\}$ (with inverse given by the antipodal map $\theta$ at $x$).
For each $t \in I$, the space $D^2 \times \{t\}$ is homeomorphic to $D^2 \times I$, hence its fundamental group is isomorphic to $\pi_1(D^2 \times I)= \pi_1(D^2) \ast \pi_1(I)$.
I’d like to conclude, using a projection theorem, that $\pi_1(X) = \pi_1(D^2) \ast \pi_1(I)$.
But I don’t know what the first fundamental group is. The point is that $\pi_1(X)= \pi_1(X \smallsetminus \partial X) \ast \pi_1(\partial X)$. So maybe I should somehow weaken $\pi_1(X \smallsetminus \partial X)$?
I’ve heard that the fundamental group of $X$ is also considered as the fundamental

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