Some may argue that monopolies become complacent with research and development because they’re got no one to compete with for the newest technology and product, but this would assume that monopolies have unconditional power which cannot be challenged or toppled. The reality is that a monopoly won’t just stop innovating because they’re the sole player in the market because to do so would leave them vulnerable to new competition. If they stopped or slowed down innovation, gaps in the market would emerge and new companies would jump at the bid to fill this gap, creating competition for the monopoly. Therefore, rather than stop innovating, monopolies are incentivised to keep innovating so that they maintain their control on the market. If they were to stop innovating, competition would arrive and they would lose their monopoly.
According to 20th century Austrian economist Joseph Schumpeter, the above average profits afforded to monopolies incentivises them to innovate.
A Schumpeterian approach to monopolies argues that greater profits lead to greater incentives to innovate – the more a company is able to profit the more innovation we (the customers) will see. Schumpeterian economics advocates to deregulated the markets to enable maximum profits, and therefore innovation.
An example of this is in the the Google search engine which has been accused of being a monopoly
Google's monopoly in the search engine market is a product of its innovation because competition exists (firefox, internet explorer, safari and so on) yet they continue to dominate the market because they's produced a superior product through spending and innovation. 
It is through rigorous innovation that Google has been able to create and maintain their search engine monopoly. They’re an example of a competitive monopoly. What’s more, their status as a monopoly has enabled this because their high profit margin allows them to invest more in innovation .
This is especially true in industries where innovation is expensive. 
These principles, however, are not universal and it is by no means guaranteed that monopolies will in fact invest more in research, development and innovation. Economic theory is rather distinct from economic practice and at the end of the day each monopoly operates differently, with different values, consumers, and practices. But to demonise monopolies and breakers of innovation is a generalisation; while it may occur in some monopolies, it is by no means the default response, and it must be appreciated that monopolies can be huge powerhouses of research and innovation. The ultimate task is to ensure that monopolies do not abuse their monopolistic powers in and over the market.