Kansas evaluates these kinds of cases, known as premises liability cases, under the general law of negligence (which is a common law claim governed by case law in Kansas, rather than a statute, except as modified by specific statutes in some respect or other).
When you own or control a piece of property, you are responsible for making reasonable efforts to ensure that visitors are safe. If you fail to identify safety risks that you should have reasonably known about, or if you fail to correct potentially hazardous conditions, you could be held liable for any injuries that result. The law is just that vague and is interpreted by judges and juries on a case by case basis.
When that happens Kansas uses a comparative negligence system that evaluates the percentage of the fault attributable to everyone who is alleged to have been negligent including the person injured. Damages are allocated based upon those percentages (unless the person injured is more than 50% at fault, in which case the person injured recovers nothing in the lawsuit).
Kansas is not among the states that make a formalistic distinction between the duties owed to "invitees", "licensees" and "trespassers" as the common law historically did. If a risk is foreseeable and you could have taken affordable precautions (relative to the value of the activity the not taking the precaution made possible) to address it, and you didn't, you could be held liable. Trespassing is just one of an infinite number of factors that the jury considers in assigning comparative fault.
The main pro-active actions that you can take are to purchase homeowner's insurance with reasonable liability policy limits and ideally umbrella insurance as well (which increases your policy limits at a modest additional cost), and to communicate in writing to the neighbor (in a way that you can prove if anything happens later) warning your neighbor of the risks that you foresee and urging your neighbor to take care to avoid those risks.
The statute of limitations in these cases in Kansas is usually two years although exceptions apply.