Papers by Parameswaran Sankaran
OSAKA JOURNAL OF MATHEMATICS
In this note we shall give a description of the K-ring of a quasi-toric manifold in terms of gene... more In this note we shall give a description of the K-ring of a quasi-toric manifold in terms of generators and relations. We apply our results to describe the K-ring of Bott-Samelson varieties.
Commentarii Mathematici Helvetici, 2003
Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C * ) n over a... more Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C * ) n over a topological space B. Let X be a nonsingular projective T -toric variety. One has the X-bundle π :
Pacific Journal of Mathematics, 2016
Let φ : Γ → Γ be an automorphism of a group Γ. We say that x, y ∈ Γ are in the same φ-twisted con... more Let φ : Γ → Γ be an automorphism of a group Γ. We say that x, y ∈ Γ are in the same φ-twisted conjugacy class and write x ∼ φ y if there exists an element γ ∈ Γ such that y = γxφ(γ −1 ). This is an equivalence relation on Γ called the φ-twisted conjugacy. Let
Pacific Journal of Mathematics, 1986
Data Revues 1631073x V349i7 8 S1631073x1100063x, Apr 1, 2011
LetL i −→ X i be a holomorphic line bundle over a compact complex manifold for i = 1, 2. Let S i ... more LetL i −→ X i be a holomorphic line bundle over a compact complex manifold for i = 1, 2. Let S i denote the associated principal circle-bundle with respect to some hermitian inner product onL i . We construct complex structures on S = S 1 × S 2 which we refer to as scalar, diagonal, and linear types. While scalar type structures always exist, diagonal type structures are constructed assuming thatL i are equivariant (C * ) n i -bundles satisfying some additional conditions. The linear type complex structures are constructed assuming X i are (generalized) flag varieties andL i negative ample line bundles over X i . When H 1 (X 1 ; R) = 0 and c 1 (L 1 ) ∈ H 2 (X 1 ; R) is non-zero, the compact manifold S does not admit any symplectic structure and hence it is non-Kähler with respect to any complex structure.
In this note we shall prove that the Stone-\v{C}ech compactification of $\mathcal{L}^n$ is the sp... more In this note we shall prove that the Stone-\v{C}ech compactification of $\mathcal{L}^n$ is the space $\bar{\mathcal{L}}^n$ where $\bar{\mathcal{L}}$ is the extended long line, namely, $\mathcal{L}$ together with its ends $\pm \Omega$. We give a similar description for the Stone-\v{C}ech compactification of the cartesian power of the semi-closed half-long line $\mathcal{L}_+$. As an application we show that any torsion subgroup of the group of all homeomorphisms of $\cj^n$ (resp. $\cl^n$) is isomorphic to a subgroup of the symmetric group $S_n$ (resp. the semidirect product $(\bz/2\bz)^n\ltimes S_n$).
Let G be any finitely generated infinite group. Denote by K(G) the FC-centre of G, i.e., the subg... more Let G be any finitely generated infinite group. Denote by K(G) the FC-centre of G, i.e., the subgroup of all elements of G whose centralizers are of finite index in G. Let QI(G) denote the group of quasi-isometries of G with respect to word metric. We observe that the natural homomorphism from the group of automorphisms of G to QI(G) is a monomorphism only if K(G) equals the centre Z(G) of G. The converse holds if K(G)=Z(G) is torsion free. We apply this criterion to many interesting classes of groups.
Let $\bar{L}_i\lr X_i$ be a holomorphic line bundle over a compact complex manifold for $i=1,2$. ... more Let $\bar{L}_i\lr X_i$ be a holomorphic line bundle over a compact complex manifold for $i=1,2$. Let $S_i$ denote the associated principal circle-bundle with respect to some hermitian inner product on $\bar{L}_i$. We construct complex structures on $S=S_1\times S_2$ which we refer to as {\em scalar, diagonal, and linear types}. While scalar type structures always exist, the more general diagonal but non-scalar type structures are constructed assuming that $\bar{L}_i$ are equivariant $(\bc^*)^{n_i}$-bundles satisfying some additional conditions. The linear type complex structures are constructed assuming $X_i$ are (generalized) flag varieties and $\bar{L}_i$ negative ample line bundles over $X_i$. When $H^1(X_1;\br)=0$ and $c_1(\bar{L}_1)\in H^2(X_1;\br)$ is non-zero, the compact manifold $S$ does not admit any symplectic structure and hence it is non-K\"ahler with respect to {\em any} complex structure. We obtain a vanishing theorem for $H^q(S;\mathcal{O}_S)$ when $X_i$ are projective manifolds, $\bar{L}_i^\vee$ are very ample and the cone over $X_i$ with respect to the projective imbedding defined by $\bar{L}_i^\vee$ are Cohen-Macaulay. We obtain applications to the Picard group of $S$. When $X_i=G_i/P_i$ where $P_i$ are maximal parabolic subgroups and $S$ is endowed with linear type complex structure with `vanishing unipotent part' we show that the field of meromorphic functions on $S$ is purely transcendental over $\bc$.
Bulletin Des Sciences Mathematiques, Jul 1, 2007
Let σ be a nontrivial automorphism of a compact connected Riemann surface X of genus at least two... more Let σ be a nontrivial automorphism of a compact connected Riemann surface X of genus at least two. Assume that σ fixes each of the theta characteristics of X. We prove that X is hyperelliptic, and σ is the unique hyperelliptic involution of X.
An arbitrary Feynman graph for string field theory interactions is analysed and the homeomorphism... more An arbitrary Feynman graph for string field theory interactions is analysed and the homeomorphism type of the corresponding world sheet surface is completely determined even in the non-orientable cases. Algorithms are found to mechanically compute the topological characteristics of the resulting surface from the structure of the signed oriented graph. Whitney's permutation-theoretic coding of graphs is utilized.
Proceedings Mathematical Sciences, Aug 1, 1991
Osaka Journal of Mathematics, May 5, 2008
Let $f:G_{n,k}\longrightarrow G_{m,l}$ be any continuous map between any two distinct complex Gra... more 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.
Bulletin des Sciences Mathématiques, 2015
Let X be a locally symmetric space Γ\G/K where G is a connected noncompact semisimple real Lie gr... more Let X be a locally symmetric space Γ\G/K where G is a connected noncompact semisimple real Lie group with trivial centre, K is a maximal compact subgroup of G, and Γ ⊂ G is a torsion-free irreducible lattice in G. Let Y = Λ\H/L be another such space having the same dimension as X. Suppose that real rank of G is at least 2.
... Work on Flag and Schubert Varieties V. Lakshmibai and C. Musili 34 Seshadri and the Cheimai M... more ... Work on Flag and Schubert Varieties V. Lakshmibai and C. Musili 34 Seshadri and the Cheimai Mathematical Institute KR Nagarajan 42 ... Abhyankar, WJ Heinzer, A. Sathaye 51 Orbits of Certain Endomorphisms of Nilmanifolds and Haus-dorff Dimension CS Aravinda and P ...
Indian Journal of Mathematics
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Papers by Parameswaran Sankaran