You seem to have some sort of engineering background. So, as of today there is no known method for time travel. Are there topological treatments of spacetime? Yes. To a small degree General Relativity can be viewed as topological description of gravity and spacetime. More closely apt is the idea that ER = EPR.
Short Answer: You might be familiar with these two Einstein-Rosen and Einstein-Podolsky-Rosen papers from 1935. "ER" is a gravitational treatment of condensed matter (black holes specifically), separated by a great distance in spacetime but linked by a wormhole. Wormholes are still theoretical 90 years later. "EPR" is a treatment of two entangled particles separated by a great distance in spacetime where measuring the quantum state of one instantly reveals the state of the other. In 2013 physicist Juan Maldacena reviewed the two papers and wrote a cryptic note to physicist Leonard Susskind: " ER= EPR". Susskind immediately got the message. The two Einstein papers, written 8 weeks apart from each other in 1935 are the same description of a single idea. One is classical (ER) and the other a quantum (EPR) description of the same thing: "Spooky action at a distance" does not violate the light speed limit if the information can take a short-cut from A to B. Certain topologies of spacetime allow for what is otherwise impossible travel through spacetime. Neither ER nor EPR suggest or even hint at time travel but it is a place for you to start.
