arXiv subjects

Swagata Sarkar

Publications and source records attributed to Swagata Sarkar.

7 recordsLinked to original sources

arXiv2025

Endomorphisms of the Cohomology Algebra of the Even Orthogonal Grassmannian

Let $M_{n,k}$ denote the even orthogonal Grassmanian, $SO(2n) / (U(k) \times SO(2n-2k) )$. We study endomorphisms of the rational cohomology algebra of $M_{n,k}$. We prove that an endomorphism of the rational cohomology algebra of $M_{n,k}$, which maps all the Chern classes of the canonical $k$-plane bundle over $M_{n,k}$ to zero, or maps all the Pontrjagin classes of the canonical, real, oriented $(2n-2k)$-plane bundle over $M_{n,k}$ to zero, is the zero endomorphism. Additionally, we prove that if an endomorphism of the rational cohomology algebra of $M_{n,k}$ vanishes on $H^{2}(M_{n,k}; \mathbb{Q})$, and admits a splitting, then the splitting equals zero.

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arXiv2025

Sense of Belonging and Intent to Persist: Mediating Role of Motivation and Moderating Role of Gender in Physics and Astronomy Graduate Students

This study investigates how graduate students' sense of belonging (SB) influences their intent to persist (IP) in physics and astronomy programs, and how this relationship is shaped by the basic psychological needs that drive motivation-autonomy, competence, and relatedness-as well as gender. Grounded in self-determination theory, the analysis treats these three needs as mediators and gender as a moderator. A quantitative survey was administered to graduate students in the Department of Physics and Astronomy at a large public land-grant R1 Midwestern university in the USA. Using probit regressions, we found that SB significantly predicts IP. Autonomy may play a compensatory role when SB is high, competence amplifies the effect of SB on IP, and relatedness buffers against low SB. Gender moderates the relationship: women report lower IP at low levels of SB but exceed men when SB is strong. These findings underscore the importance of fostering a sense of belonging, academic confidence, and social connection-particularly for women in male-dominated STEM fields.

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arXiv2022

$p$-local decompositions of projective Stiefel manifolds

The main objective of this paper is to analyze the $p$-local homotopy type of the complex projective Stiefel manifolds, and other analogous quotients of Stiefel manifolds. We take the cue from a result of Yamaguchi about the $p$-regularity of the complex Stiefel manifolds which lays down some hypotheses under which the Stiefel manifold is $p$-locally a product of odd dimensional spheres. We show that in many cases, the projective Stiefel manifolds are $p$-locally a product of a complex projective space and some odd dimensional spheres. As an application, we prove that in these cases, the $p$-regularity result of Yamaguchi is also $S^1$-equivariant.

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arXiv2015

Degrees of Maps between Isotropic Grassmann Manifolds

Let $\widetilde{I}_{2n,k}$ denote the space of $k$-dimensional, oriented isotropic subspaces of $\mathbb{R}^{2n}$, called the oriented isotropic Grassmannian. Let $f \colon \widetilde{I}_{2n,k} \rightarrow \widetilde{I}_{2m,l} $ be a map between two oriented isotropic Grassmannians of the same dimension, where $k,l \geq 2$. We show that either $(n,k) = (m,l)$ or the degree of $f$ must be zero. Let $\mathbb{R}\widetilde{G}_{m,l}$ denote the oriented real Grassmann manifold. For $k,l \geq 2$ and $\dim{\widetilde{I}_{2n,k}} = \dim{\mathbb{R}\widetilde{G}_{m,l}}$, we also show that the degree of maps $g \colon \mathbb{R} \widetilde{G}_{m,l} \rightarrow \widetilde{I}_{2n,k} $ and $h \colon \widetilde{I}_{2n,k} \rightarrow \mathbb{R} \widetilde{G}_{m,l}$ must be zero.

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arXiv2013

Some Computations in Equivariant cobordism in relation to Milnor manifolds

Let $\mathcal{N}_*$ be the unoriented cobordism algebra, let $G=(\Z_2)^n$ and let $Z_*(G)$ denote the equivariant cobordism algebra of $G$-manifolds with finite stationary point sets. Let $ε_* :Z_*(G) \to \mathcal{N}_*$ be the homomorphism which forgets the $G$-action. We use Milnor manifolds (degree 1 hypersurfaces in $\R P^m\times \R P^n$) to construct non-trivial elements in $Z_*(G)$. We prove that these elements give rise to indecomposable elements in $Z_*(G)$ in degrees up to $2^n - 5$. Moreover, in most cases these elements can be arranged to be in $\mathit{Ker}(ε_*)$.

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arXiv2013

Finite group actions on Kan complexes

We study simplicial action of groups on one vertex Kan complexes. We show that every semi-direct product of the fundamental group of an one vertex Kan complex with a finite group can be simplicially realized. We also calculate the cohomology of the fixed point set of a finite $p-$group action on an one vertex aspherical Kan complex.

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arXiv2008

Degrees of maps between Grassmann manifolds

Let $f:G_{n,k}\longrightarrow G_{m,l}$ be any continuous map between any two distinct complex Grassmann manifolds of the same dimension where the target is not the complex projective space. We show that, for any given $k,l$, the degree of $f$ is zero provided that $m,n$ are sufficiently large. If the degree of $f$ is $\pm 1$, we show that $(m,l)=(n,k)$ and $f$ is a homotopy equivalence. Also, we prove that the image under $f^*$ of elements of a set of algebra generators of $H^*(G_{m,l};\mathbb{Q})$ is determined upto a sign, $\pm$, if the degree of $f$ is non-zero. Our proofs cover the case of quaternionic Grassmann manifolds as well.

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