> Switzerland is mountainous in parts. Here's a topographical map [1].

I looked at your map and I am aware of the alps. Even a small amount of mountains can present serious problems for a military invasion and we are talking about the Swiss Alps. That is, one of the most impassable geographic boundaries in Europe. I am surprised I have to say this, the Swiss Alps are a massive defensive benefit to Switzerland.

> Also looking a population map [2] and you'll see those mountainous areas are largely uninhabited.

I think you have misunderstood the benefit of mountains to Swiss defense. People don't need to live in the mountains. Rather the mountains provide bottlenecks and choke points that prevent an attacker from leveraging their numerical advantage. Mountain roads often force the use of narrow columns which are vulnerable to ambush or barricades. Mountains provide excellent vantage points to shell roads and bottlenecks. Mountains provide some protection against airpower.

That that being said, Switzerland is not impossible to invade. During the early stages of a conflict like WW2 the cost of invasion is greater than the benefit, but it Germany had defeated the Soviet Union a successful Swiss invasion would be likely. Moving troops through Switzerland is slow so taking it to open a second front in the early stages of a war against say France doesn't provide much benefit.

> The border between Geneva and France isn't a natural border of any kind.

I agree Geneva which is only 4 miles from France and it does not have much geographic protection. If Switzerland is attacked by the French, they will capture Geneva. That doesn't mean that mountains do not provide Switzerland a massive defensive benefit especially to threats from the North or East.

> The US would never accept Chinese or Russian military bases in Canada or Mexico (and nearly started a nuclear war about Russian missiles in Cuba) but can't see how Russia might have the exact same strategic concerns.

Europe accepts Kaliningrad a Russian military base on occupied German land. The US has yet to invade Cuba.

The purpose of the invasion Ukraine as stated by the Russian government in a victory statement they accidentally published is not mostly not about NATO, if anything the invasion of Ukraine increases NATOs power. Rather the invasion is about the creation of Slavic ethno-nationalist super state [0]. The Russian government statement says in part:

"Russia is restoring its unity - the tragedy of 1991, this terrible catastrophe in our history, its unnatural dislocation, has been overcome. Yes, at a great cost, yes, through the tragic events of a virtual civil war, because now brothers, separated by belonging to the Russian and Ukrainian armies, are still shooting at each other, but there will be no more Ukraine as anti-Russia. Russia is restoring its historical fullness, gathering the Russian world, the Russian people together - in its entirety of Great Russians, Belarusians and Little Russians. If we had abandoned this, if we had allowed the temporary division to take hold for centuries, then we would not only betray the memory of our ancestors" [0]

It goes on to say that NATO is only a secondary concern, the primary concern is one of blood and soil:

"Vladimir Putin has assumed, without a drop of exaggeration, a historic responsibility by deciding not to leave the solution of the Ukrainian question to future generations. After all, the need to solve it would always remain the main problem for Russia - for two key reasons. And the issue of national security, that is, the creation of anti-Russia from Ukraine and an outpost for the West to put pressure on us, is only the second most important among them.

The first would always be the complex of a divided people, the complex of national humiliation - when the Russian house first lost part of its foundation (Kiev), and then was forced to come to terms with the existence of two states, not one, but two peoples. That is, either to abandon their history, agreeing with the insane versions that "only Ukraine is the real Russia," or to gnash one's teeth helplessly, remembering the times when "we lost Ukraine." [0]

This article aligns which many of the things which Putin has been saying for years so it seems that it credibly represents the reasons for the invasion in Putin's mind. Putin is chasing an imperial dream. He wants glory for himself and a legacy.

[0]: "The offensive of Russia and the new world", Russian Agency of International Information, - https://web.archive.org/web/20220226051154/https://ria.ru/20... translation--> https://web-archive-org.translate.goog/web/20220226051154/ht...