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Biplab Basak

Visiting Scholar, SERB Indo-US Postdoctoral Fellow

Overview

Research Focus

My research interests are focused on the study of topological, geometric and combinatorial properties of cell complexes which are manifolds, especially crystallizations. The original concept of crystallization is that of "contracted triangulation", which was introduced with the main goal of nding a "minimal" atlas for topological manifolds. Only later did the possibility of using graph-theoretical tools for representing PL manifolds become a major aspect of the theory. Within crystallization theory, two interesting PL invariants for d-manifolds have been introduced and studied, namely gem-complexity and regular genus. Currently, I am working on the gem-complexity and regular genus of PL d-manifolds.

Departments/Programs

  • Mathematics

Publications

  • 3-Regular Colored Graphs and Classification of Surfaces, Discrete Comput. Geom. (2017), 58 (2) (2017), 345-354.
  • Lower bounds for regular genus and gem-complexity of PL 4-manifolds (with M. R. Casali), Forum Math., 29 (4) (2017), 761-773.
  • An algorithmic approach to construct crystallizations of 3-manifolds from presentations of fundamental groups, Proc. Indian Acad. Sci. (Math. Sci.) 126 (4) (2016), 629-653.
  • Simple crystallizations of 4-manifolds (with J. Spreer), Adv. Geom. 16 (1) (2016), 111-130.
  • Equivariant and equilibrium triangulations of some small covers with the minimum number of vertices (with S. Sarkar), J. Ramanujan Math. Soc., 30, (1) (2015), 29-50.
  • Minimal crystallizations of 3-manifolds (with B. Datta), Electron. J Combin. 21 (1) (2014), #P1.61, 1-25.