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PCWins.com is not responsible for the content of any linked site or any link contained in a linked site, or transactions conducted via such links. The inclusion of these links is only for the convenience of users. If you continue without changing your settings, you agree to our use of cookies.1. Technical Field
The present disclosure generally relates to controlling a power conversion device with an overcurrent protection mechanism.
2. Description of Related Art
In a power conversion device, overcurrent protection mechanism controls a switch. However, the timing of the overcurrent protection mechanism is limited, which affects the power conversion effect.
Therefore, there is room for improvement in the art.
The present disclosure is related to a power conversion device having an overcurrent protection mechanism.Q:

Fundamental group of $S^1 times S^2$

I’m trying to compute the fundamental group of $S^1 times S^2$. I know that $S^1 times S^2 approx S^1 vee S^1$ via the inclusion $iota$ of each factor in the wedge sum. Since the inclusion $iota$ induces an isomorphism on homotopy groups, it induces an isomorphism on fundamental groups. However, using Whitehead’s theorem, I’ve found that there are many counter-examples to the isomorphism on fundamental groups (take the inclusion $S^1 subset S^1 vee S^1$ as a counterexample). What am I missing here?

A:

I guess it is a “folklore” fact that the fundamental group of a wedge of $S^1$’s is $mathbb Zoplusmathbb Z$, though I’ve not seen this written down.
When you take the wedge of $S^1$’s you are adding a disc to each $S^1$ and the disc is attached to the last $S^1$. If you take the first $S^1$ as the base point, the fundamental group is $mathbb Z$, if you take the second $S^1$ as base point, the fundamental group is $mathbb Zoplus mathbb Z$: This is just the fundamental group of the circle and can be obtained

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