What's the name of this green fruit with little pikes fallen from a city tree on the pavement?
It is horse chestnut it is very common to plant chestnut trees in public parks and a lot of people do have them around their property and by the side of many roads.
What you have in your picture is the fruit and the leaves on the ground confirms that this is horse chestnut.
Source https://en.wikipedia.org/wiki/Aesculus_hippocastanum
The nut is poisonus and the toxin can cause loss of coordination and tremors in horses if they eat the nuts.
Touching or handling the nuts do not cause any adverse effect to humans they are only dangerous to humans if they are eaten.
Horse chestnut contains alcaloid saponins and glucosides that have a toxic effect on mamals.