13 citations · 50 across the 15 of their papers we have counts for
18 papers
On manifolds homeomorphic to spheres
Somnath Basu, Sachchidanand Prasad
We prove a result analogous to Reeb's theorem in the context of Morse-Bott functions: if a closed, smooth manifold admits a Morse-Bott function having two critical submanifolds…
On the generalized brace product: relation to -splitting of loop space fibrations \& the -homomorphism
Somnath Basu, Aritra Bhowmick, Sandip Samanta
Given a fibration with a homotopy section , James introduced a binary product $\left\{, \right\}_s: π_i B \times π_j F \righ…
Graph Polynomial for Colored Embedded Graphs: A Topological Approach
Somnath Basu, Dhruv Bhasin, Siddhartha Lal +1
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological wh…
Equivalence Between Four Models of Associahedra
Somnath Basu, Sandip Samanta
We present a combinatorial isomorphism between Stasheff associahedra and an inductive cone construction of those complexes given by Loday. We give an alternate description of certa…
Unveiling topological order through multipartite entanglement
Siddhartha Patra, Somnath Basu, Siddhartha Lal
It is well known that the topological entanglement entropy () of a topologically ordered ground state in 2 spatial dimensions can be captured efficiently by measuring the…
A connection between cut locus, Thom space and Morse-Bott functions
Somnath Basu, Sachchidanand Prasad
Associated to every closed, embedded submanifold in a connected Riemannian manifold , there is the distance function which measures the distance of a point in from…
Counting curves in a linear system with upto eight singular points
Somnath Basu, Ritwik Mukherjee
In this paper, we develop a systematic approach to enumerate curves with a certain number of nodes and one further singularity which maybe more degenerate. As a result, we obtain a…
On the cohomology ring and upper characteristic rank of Grassmannian of oriented -planes
Somnath Basu, Prateep Chakraborty
In this paper we study the mod cohomology ring of the Grasmannian of oriented -planes in . We determine the degrees of the indecomposable…
Homotopy groups of certain highly connected manifolds via loop space homology
Samik Basu, Somnath Basu
For we consider -connected closed manifolds of dimension at most . We prove that away from a finite set of primes, the -local homotopy groups of are…
Realizing congruence subgroups inside the diffeomorphism group of a product of homotopy spheres
Somnath Basu, Thomas Farrell
Let M be a smooth manifold which is homeomorphic to the n-fold product of S^k, where k is odd. There is an induced homomorphism from the group of diffeomorphisms of M to the automo…
Homotopy groups of highly connected manifolds
Samik Basu, Somnath Basu
In this paper we give a formula for the homotopy groups of -connected -manifolds as a direct sum of homotopy groups of spheres in the case the Betti number is l…
Nambu Structures And Associated Bialgebroids
Samik Basu, Somnath Basu, Apurba Das +1
This paper investigates higher order generalizations of well known results for Lie algebroids and bialgebroids. It is proved that -Lie algebroid structures correspond to -ary…
Counting curves on a general linear system with up to two singular points
Somnath Basu, Ritwik Mukherjee
In this paper we obtain an explicit formula for the number of curves in a compact complex surface (passing through the right number of generic points), that has up to one node…
Enumeration of curves with two singular points
Somnath Basu, Ritwik Mukherjee
In this paper we obtain an explicit formula for the number of curves in two dimensional complex projective space, of degree d, passing through d(d+3)/2-(k+1) generic points and hav…
Enumeration of curves with one singular point
Somnath Basu, Ritwik Mukherjee
In this paper we obtain an explicit formula for the number of degree d curves in two dimensional complex projective space, passing through (d(d+3)/2 -k) generic points and having a…
Homotopy groups and periodic geodesics of closed 4-manifolds
Samik Basu, Somnath Basu
Given a simply connected, closed four manifold, we associate to it a simply connected, closed, spin five manifold. This leads to several consequences : the stable and unstable homo…
Transverse string topology and the cord algebra
Somnath Basu, Jason McGibbon, Dennis Sullivan +1
We define a coalgebra structure for open strings transverse to any framed codimension 2 submanifold. When the submanifold is a knot in R^3, we show this structure recovers a specia…
Of Sullivan models, Massey products, and twisted Pontrjagin products
Somnath Basu
Associated to every connected, topological space there is a Hopf algebra - the Pontrjagin ring of the based loop space of the configuration space of two points in X. We prove t…