Biplab Basak

activity

20132026

most citedSimple crystallizations of 4-manifolds

17 citations · 68 across the 30 of their papers we have counts for

collaborators

32 papers

math.CO2026

The Homotopy Types of the Independence and Perfect Matching Complexes of Möbius and Circular Ladder Graphs

Anshu Agarwal, Biplab Basak

The independence complex and perfect matching complex of a graph are simplicial complexes encoding, respectively, its independent sets and perfect matchings. Determining their homo…

math.CO2026

A Complete Classification of Discrete $d$ -Pseudomanifolds with at Most $2 d + 7$ Vertices

Biplab Basak, Debolina Ghosh, Raju Kumar Gupta

A simple undirected graph $M$ is called a discrete $d$ -pseudomanifold if, for every vertex $v$ , the induced subgraph $N_{M} (v)$ on the neighbors of $v$ is a discrete $(d - 1)$ -pseudoma…

math.CO2026

Coloring discrete pseudomanifolds

Biplab Basak, Vanny Doem, Chandal Nahak

This paper presents three main results on coloring discrete $d$ -pseudomanifolds: $(1)$ the general chromatic bounds $d + 1 \leq X (K) \leq 2 d + 2$ for any $d$ -pseudomanifold $K$ ; $(2)$ …

math.GT2025

A classification of semi-equivelar gems on the double torus

Anshu Agarwal, Biplab Basak, Debolina Ghosh

A \emph{semi-equivelar gem} of a PL $d$ -manifold is a regular colored graph that represents the manifold and admits a regular embedding on a surface, such that the cyclic sequence…

math.GT2025

Regular genus of $S^{2} \times S^{1} \times S^{1}$ , $4$ -torus, and small covers over $Δ^{2} \times Δ^{2}$

Anshu Agarwal, Biplab Basak

A crystallization of a PL manifold is an edge-colored graph encoding a contracted triangulation of the manifold. The concept of regular genus generalizes the notions of surface gen…

math.CO2025

Normal $4$ -pseudomanifolds with a relative 2-skeleton

Biplab Basak, Mangaldeep Saha, Sourav Sarkar

The study of face-number-related invariants in simplicial complexes is a central topic in combinatorial topology. Among these, the invariant $g_{2}$ plays a significant role. For a n…

math.CO2025

Minimal Simplicial Degree $d$ Maps from Genus $g$ Surfaces to the Torus

Biplab Basak, Ayushi Trivedi

The degree of a map between orientable manifolds is a fundamental concept in topology, offering deep insights into the structure of the manifolds and the nature of the correspondin…

math.GT2025

Embeddings of edge-colored dual graphs of balanced 3- and 4-manifolds

Biplab Basak, Sourav Sarkar

This article focuses on a class of properly edge-colored graphs, which arise from topological combinatorics, and investigates their embeddings onto surfaces. Specifically, these gr…

math.GT2024

Simplicial degree $d$ self-maps on $n$ -spheres

Biplab Basak, Raju Kumar Gupta, Ayushi Trivedi

The degree of a map between orientable manifolds is a fundamental concept in topology, providing deep insights into the structure of manifolds and the behavior of maps between them…

math.GT2024

Crystallizations of small covers over the $n$ -simplex $Δ^{n}$ and the prism $Δ^{n - 1} \times I$

Anshu Agarwal, Biplab Basak

A crystallization of a PL manifold is an edge-colored graph that corresponds to a contracted triangulation of the manifold, facilitating the study of its topological and combinator…

math.GT2024

Minimal simplicial degree $d$ self-maps of $S^{n - 1} \times S^{1}$

Anshu Agarwal, Biplab Basak, Sourav Sarkar

The degree of a map between orientable manifolds is a fundamental concept in topology, providing important information about the structure of manifolds and the behavior of maps bet…

math.CO2024

Average edge order of normal $3$ -pseudomanifolds

Biplab Basak, Raju Kumar Gupta

In their work [10], Feng Luo and Richard Stong introduced the concept of the average edge order, denoted as $μ_{0} (K)$ . They demonstrated that if $μ_{0} (K) \leq \frac{9}{2}$ for a close…

math.CO2024

A classification of semi-equivelar gems of PL $d$ -manifolds on the surface with Euler characteristic $- 1$

Anshu Agarwal, Biplab Basak

A semi-equivelar gem of a PL $d$ -manifold is a regular colored graph that represents the PL $d$ -manifold and regularly embeds on a surface, with the property that the cyclic sequen…

math.GT2023★ 1 cited

A structure theorem for homology 4-manifolds with $g_{2} \leq 5$

Biplab Basak, Sourav Sarkar

Numerous structural findings of homology manifolds have been derived in various ways in relation to $g_{2}$ -values. The homology $4$ -manifolds with $g_{2} \leq 5$ are characterized comb…

math.CO2022

Semi-equivelar gems of PL $d$ -manifolds

Biplab Basak, Manisha Binjola

We define the notion of $(p_{0}, p_{1}, \dots, p_{d})$ -type semi-equivelar gems for closed connected PL $d$ -manifolds, related to the regular embedding of gems $Γ$ representing $M$ on a sur…

math.CO2022

On a construction of some homology $d$ -manifolds

Biplab Basak, Sourav Sarkar

The $g$ -vector of a simplicial complex contains a lot of information about the combinatorial and topological structure of that complex. Several classification results regarding the…

math.CO2022

A characterization of normal $3$ -pseudomanifolds with $g_{2} \leq 4$

Biplab Basak, Raju Kumar Gupta

We characterize normal $3$ -pseudomanifolds with $g_{2} \leq 4$ . We know that if a $3$ -pseudomanifold with $g_{2} \leq 4$ does not have any singular vertices then it is a $3$ -sphere. We fir…

math.CO2022★ 2 cited

A characterization of $g_{2}$ -minimal normal 3-pseudomanifolds with at most four singularities

Biplab Basak, Raju Kumar Gupta, Sourav Sarkar

Let $Δ$ be a $g_{2}$ -minimal normal 3-pseudomanifold. A vertex in $Δ$ whose link is not a sphere is called a singular vertex. When $Δ$ contains at most two singular vertices, its com…

math.GT2021★ 3 cited

A characterization of normal 3-pseudomanifolds with at most two singularities

Biplab Basak, Raju Kumar Gupta, Sourav Sarkar

Characterizing face-number-related invariants of a given class of simplicial complexes has been a central topic in combinatorial topology. In this regard, one of the well-known inv…

math.GT2021

Handle decompositions for a class of closed orientable PL 4-manifolds

Biplab Basak, Manisha Binjola

In this article, we study a class of closed connected orientable PL $4$ -manifolds admitting a semi-simple crystallization and which have an infinite cyclic fundamental group. We sh…

math.GT2020

On regular genus and G-degree of PL 4-manifolds with boundary

Biplab Basak, Manisha Binjola

In this article, we introduce two new PL-invariants: weighted regular genus and weighted G-degree for manifolds with boundary. We first prove two inequalities involving some PL-inv…

math.GT2020★ 1 cited

Lower bounds for regular genus and gem-complexity of PL 4-manifolds with boundary

Biplab Basak, Manisha Binjola

Let $M$ be a connected compact PL 4-manifold with boundary. In this article, we have given several lower bounds for regular genus and gem-complexity of the manifold $M$ . In particu…

math.GT2020★ 2 cited

Minimal crystallizations of 3-manifolds with boundary

Biplab Basak, Manisha Binjola

Let $(Γ, γ)$ be a crystallization of connected compact 3-manifold $M$ with $h$ boundary components. Let $G (M)$ and $k (M)$ be the regular genus and gem-complexity…

math.GT2018★ 9 cited

Three-dimensional normal pseudomanifolds with relatively few edges

Biplab Basak, Ed Swartz

Let $Δ$ be a $d$ -dimensional normal pseudomanifold, $d \geq 3.$ A relative lower bound for the number of edges in $Δ$ is that $g_{2}$ of $Δ$ is at least $g_{2}$ of the link of any verte…

The Homotopy Types of the Independence and Perfect Matching Complexes of Möbius and Circular Ladder Graphs

A Complete Classification of Discrete d-Pseudomanifolds with at Most 2d+7 Vertices

Coloring discrete pseudomanifolds

A classification of semi-equivelar gems on the double torus

Regular genus of S2×S1×S1, 4-torus, and small covers over Δ2×Δ2

Normal 4-pseudomanifolds with a relative 2-skeleton

Minimal Simplicial Degree d Maps from Genus g Surfaces to the Torus

Embeddings of edge-colored dual graphs of balanced 3- and 4-manifolds

Simplicial degree d self-maps on n-spheres

Crystallizations of small covers over the n-simplex Δn and the prism Δn−1×I

Minimal simplicial degree d self-maps of Sn−1×S1

Average edge order of normal 3-pseudomanifolds

A classification of semi-equivelar gems of PL d-manifolds on the surface with Euler characteristic −1

A structure theorem for homology 4-manifolds with g2​≤5

Semi-equivelar gems of PL d-manifolds

On a construction of some homology d-manifolds

A characterization of normal 3-pseudomanifolds with g2​≤4

A characterization of g2​-minimal normal 3-pseudomanifolds with at most four singularities

A characterization of normal 3-pseudomanifolds with at most two singularities

Handle decompositions for a class of closed orientable PL 4-manifolds

On regular genus and G-degree of PL 4-manifolds with boundary

Lower bounds for regular genus and gem-complexity of PL 4-manifolds with boundary

Minimal crystallizations of 3-manifolds with boundary

Three-dimensional normal pseudomanifolds with relatively few edges

A Complete Classification of Discrete $d$ -Pseudomanifolds with at Most $2 d + 7$ Vertices

Regular genus of $S^{2} \times S^{1} \times S^{1}$ , $4$ -torus, and small covers over $Δ^{2} \times Δ^{2}$

Normal $4$ -pseudomanifolds with a relative 2-skeleton

Minimal Simplicial Degree $d$ Maps from Genus $g$ Surfaces to the Torus

Simplicial degree $d$ self-maps on $n$ -spheres

Crystallizations of small covers over the $n$ -simplex $Δ^{n}$ and the prism $Δ^{n - 1} \times I$

Minimal simplicial degree $d$ self-maps of $S^{n - 1} \times S^{1}$

Average edge order of normal $3$ -pseudomanifolds

A classification of semi-equivelar gems of PL $d$ -manifolds on the surface with Euler characteristic $- 1$

A structure theorem for homology 4-manifolds with $g_{2} \leq 5$

Semi-equivelar gems of PL $d$ -manifolds

On a construction of some homology $d$ -manifolds

A characterization of normal $3$ -pseudomanifolds with $g_{2} \leq 4$

A characterization of $g_{2}$ -minimal normal 3-pseudomanifolds with at most four singularities