I was reading around the web and found an interesting idea for an online software that I would like to publish commercially. My question is if the software is based off of research such as https://arxiv.org/pdf/1409.3215.pdf (just an example) am I able to develop and sell it commercially? Are their legal complications?
The ideas and facts revealed in that (or any other) published article are not protected by copyright. A publication might report a patentable claim, so you have to check with the patent office to see if a thing or method described in an article has been patented. Timing matters on publishing and patenting: you can't receive a patent for something that's "out there" (because you described it in an earlier publication).