Neglecting others means ignoring [them].
I think you mean an object there, or the sentence would sound odd to my ear. In most cases where the gerund or infinite is the subject of object of a verb, you can replace one with the other (I can't think of an exception).
However, a gerund can be the object of a preposition, while an infinite normally cannot:
After conquering Athens, Augustus paused.
After *to conquer Athens...
There are also many verbs that only take one or the other. Lastly, there are cases where the two have different meanings:
Cleopatra stopped looking at Marc Athony. = "She had been looking at him but now began doing something else."
Cleopatra stopped to look at Marc Athony. = "She stopped doing whatever she was doing in order to look at him."
