Carts.

carts Piotr says,

I know that archaeologists specialising in European neolithic cultures tend to believe that carts were invented in Central Europe in the mid-4th millennium BC.

While I'd like a clearer definition of 'Central Europe', I confess an attachment to the idea myself.
First, a cart in English and in western IE means a two-wheeled, single-axled vehicle. This is distinguished from a wagon, which has two axles, each with two wheels. The cart-word is the one that also gives us chariot and car. I'm unfamiliar with the eastern IE term for carts.
The thing about wheeled vehicles is not so much the idea as it is the practical necessities. You need a variety of woods to construct a good cart, plus the necessary tools (a copper axe and copper adze can do the job, but bronze tools are much much better). The wood was plentiful in the Northern European Forest. The question is where -- and when -- did they get their tools, especially the bronze ones.
Beyond this, I can only speculate. I'd like to know what kinds of wood make up an early bronze-age vehicle. I'd bet it was made of several kinds. Hardwood for at least the axle (preferably oak), and for the wheels too. For the rest of the vehicle, you'd use lighter, easier-to-work woods, and for the sides of the vehicle, just a lightweight wicker surround is all you'd really want.
It's my belief that the IE big-bang is directly related to the technology associated with wheeled vehicles. This includes the necessary knowledge and technology to build the vehicle, plus the equally important knowledge of animal handling. This latter includes such things as harnesses, and quite clearly 'cord' -- as in the cord that decorated corded ware. This would have been hemp. I would not be the least suprised if it turned out that, on a site-by-site basis, the arrival of hemp processing technology is exactly co-eval with that of the arrival of the Corded Ware horizon. Without rope you are severely limited in how well you can handle livestock, particularly cattle and horses.
Vehicles were drawn by cattle first; everything I've read says the oldest carts were extremely heavy and rather inefficiently designed, and required the strength of an ox to pull them, something a horse could not do, and would not be able to do until the advent of the lightweight, spoke-wheeled chariot.
Rope-making and the need for a place to plant and process hemp. Bronze tools and a place to get them. Carpentry and the need for a variety of wood. Cattle-handling and the need for pastures. What kind of answer do you get from the geographical equation? I say: Kiev. The IEs, then, exploited both the grass of the steppe, and the resources of the southern edge of the Northern European Forest.
In this scenario, it's just possible the PIEs (including Anatolian) originated in the forest, at its southern edge. While it would seem they participated in the Yamna (pit grave) culture, it's not required for them to have originated it. Rather, it would be the IEs who perfected it, combining oxen-drawn vehicles, horseback riding, hemp processing, etc, for the emerging steppe culture they would dominate, while at the same time, different groups moved further into the northern forest, away from the steppe. But, as they spoke the same language, or at least, a reasonably mutually intelligible dialect, passably friendly trade relations probably existed.
I need to post my thoughts on the role of hemp -- Cannibis ssp -- and it's role in IE culture. Pressed Ephedra mixed with Cannibis would seem to be the ingredients for soma/haoma.
Mark.