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pro vyhledávání: '"Basak, Biplab"'
The degree of a map between orientable manifolds is a crucial concept in topology, providing deep insights into the structure and properties of the manifolds and the corresponding maps. This concept has been thoroughly investigated, particularly in t
Externí odkaz:
http://arxiv.org/abs/2409.00907
Autor:
Agarwal, Anshu, Basak, Biplab
A small cover is a closed manifold $M^n$ with a locally standard $\mathbb{Z}_2^n$-action such that its orbit space is a simple convex polytope $P^n$. In this article, we study the crystallizations of small covers over the $n$-simplex $\Delta^n$ and t
Externí odkaz:
http://arxiv.org/abs/2408.05922
The degree of a map between orientable manifolds is a fundamental concept in topology that aids in understanding the structure and properties of the manifolds and the maps between them. Numerous studies have been conducted on the degree of maps betwe
Externí odkaz:
http://arxiv.org/abs/2407.10128
Autor:
Basak, Biplab, Gupta, Raju Kumar
In their work [9], Feng Luo and Richard Stong introduced the concept of the average edge order, denoted as $\mu_0(K)$. They demonstrated that if $\mu_0(K)\leq \frac{9}{2}$ for a closed $3$-manifold $K$, then $K$ must be a sphere. Building upon this f
Externí odkaz:
http://arxiv.org/abs/2406.14010
Autor:
Agarwal, Anshu, Basak, Biplab
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 sequence of degrees of faces in the embedding around each vertex is identica
Externí odkaz:
http://arxiv.org/abs/2405.04005
Autor:
Basak, Biplab, Sarkar, Sourav
Publikováno v:
Adv. in Appl. Math. 157 (2024), Paper No. 102705, 26 pp
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 combinatorially in this article. It is well-known that all homology $4$-ma
Externí odkaz:
http://arxiv.org/abs/2302.02355
Autor:
Basak, Biplab, Binjola, Manisha
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 $\Gamma$ representing $M$ on a surface $S$ such that the face-cycles at all the vertices of $\Gamma
Externí odkaz:
http://arxiv.org/abs/2207.01812
Autor:
Basak, Biplab, Sarkar, Sourav
The $g$-vector of a simplicial complex contains a lot of informations about the combinatorial and topological structure of that complex. So far several classification results on the structure of normal pseudomanifolds and homology manifolds have been
Externí odkaz:
http://arxiv.org/abs/2206.01117
Autor:
Basak, Biplab, Gupta, Raju Kumar
We characterize normal $3$-pseudomanifolds with $g_2\leq4$. We know that if a $3$-pseudomanifold with $g_2\leq4$ does not have any singular vertices then it is a $3$-sphere. We first prove that a normal $3$-pseudomanifold with $g_2\leq4$ has at most
Externí odkaz:
http://arxiv.org/abs/2202.06638
Let $\Delta$ be a $g_2$-minimal normal 3-pseudomanifold. A vertex in $\Delta$ whose link is not a sphere is called a singular vertex. When $\Delta$ contains at most two singular vertices, its combinatorial characterization is known [9]. In this artic
Externí odkaz:
http://arxiv.org/abs/2202.06582