Gadgil, Siddhartha; PANDIT, SUHAS(Indian Academy of Sciences, 2010-08)
Splittings of a free group correspond to embedded spheres in the 3-manifold M = # k S 2 × S 1. These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of ...
Gadgil, Siddhartha; TADIPATRI, ANAND(Indian Academy of Sciences, 2022-05)
Tarski showed in the 1950s that (first-order) questions in Euclidean geometry could be answered algorithmically. Algorithms for doing this have greatly improved over the decades but still have high complexity (in terms of ...