Research Interests
Differential and algebraic topology and their interactions with differential geometry. Especially : the surgery classification of high-dimensional manifolds and their smooth structures, the study of exotic smooth structures and geometric (curvature, symplectic, complex and Kahler) structures on manifolds, group actions on exotic spheres, stable (co)homotopy theory and the construction of exotic smooth structures via the inertia group, the homotopy inertia group and the concordance inertia group of manifolds.
Submitted/posted papers
- with Samik Basu : Inertia Groups and Smooth Structures on Quaternionic Projective Space, arXiv:1708.06582.
- Smooth Structures on Complex Projective Spaces, arXiv:1701.07592.
Published papers
- with Samik Basu : Inertia Groups of Higher-Dimensional Complex Projective Spaces, Algebraic and Geometric Topology 18 (2018) 387-408. arXiv:1510.02636.
- Homotopy Inertia Groups and Tangential Structures, JP Journal of Geometry and Topology 20 (2), (2017) 91-114, arXiv:1511.03802.
- Smooth Structures on a Fake Projective Space, Topology Appl. 206 (2016) 1-7, arXiv:1510.03037.
- The Classification of Smooth Structures on a Homotopy Complex Projective Space, Proc. Indian Acad. Sci. (Math. Sci.), Vol. 126, No. 2 (2016), 277–281, arXiv:1510.03032.
- Inertia Groups and Smooth Structures of $(n-1)$-connected $2n$-manifolds, Osaka J. Math., Vol 53, No. 2 (2016), 309-319, arXiv:1510.03031.
- Farrell-Jones Spheres and Inertia Groups of Complex Projective Spaces, Forum Math. 27 (2015), no. 5, 3005-3015, arXiv:1510.03029.
Surveys articles
- Topological Rigidity Problems, Journal of Advanced Studies in Topology, Vol. 7, No. 4 (2016), 161-204, arXiv:1510.04139.
- A Survey of Smooth and PL-Rigidity Problems on Locally Symmetric Spaces, Journal of Advanced Studies in Topology , Vol. 7, No. 4 (2016), 205-250, arXiv:1510.04140.
Dissertation: IIT Bombay 2015