Related papers: A note on torus actions and the Witten genus

In this note, we prove that the Witten genus of nonsingular string complete intersections in product of complex projective spaces vanishes. Our result generalizes a known result of Landweber and Stong (cf. [HBJ]).

Let $\mathcal{M}_{0}^n$ be the class of closed, simply-connected, non-negatively curved Riemannian manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if $M\in \mathcal{M}_{0}^n$, then $M$ is…

We consider a Hamiltonian action of n-dimensional torus, T^n, on a compact symplectic manifold (M,\omega) with d isolated fixed points. For every fixed point p there exists (though not unique) a class a_p in H^*_{T}(M; Q) such that the…

We present some classification results for quasitoric manifolds (M) with (p_1(M)=-\sum a_i^2) for some (a_i\in H^2(M)) which admit an action of a compact connected Lie-group (G) such that (\dim M/G \leq 1). In contrast to Kuroki's work we…

We study complete, connected and simply connected $n$-dim Riemannian manifold $M$ satisfying Ricci curvature lower bound. Further more, suppose that $M$ admits discrete isometric group actions $G$ so that the diameter of the quotient space…

We associate a root system to a finite set in a free abelian group and prove that its irreducible subsystem is of type A, B or D. We apply this general result to a torus manifold, where a torus manifold is a $2n$-dimensional connected…

Motivated by a problem of Hirzebruch, we study $8$-dimensional, closed, symplectic manifolds having a Hamiltonian torus action with isolated fixed points and second Betti number equal to $1$. Such manifolds are automatically positive…

Let $M$ be a symplectic manifold, equipped with a Hamiltonian action of a torus $T$. We give an explicit formula for the rational cohomology ring of the symplectic quotient $M//T$ in terms of the cohomology ring of $M$ and fixed point data.…

Let $M$ be a $Spin$-manifold with $S^1$-action and let $\sigma \in S^1$ be of finite order. We show that the indices of certain twisted Dirac operators vanish if the action of $\sigma $ has sufficiently large fixed point codimension. These…

Let M be a connected compact pseudoRiemannian manifold acted upon topologically transitively and isometrically by a connected noncompact simple Lie group G. If m_0, n_0 are the dimensions of the maximal lightlike subspaces tangent to M and…

We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces. Our proof uses sheaves of groupoids of Hamiltonian…

The action of a torus group $T$ on a symplectic toric manifold $(M,\omega)$ often extends to an effective action of a (non-abelian) compact Lie group $G$. We may think of $T$ and $G$ as compact Lie subgroups of the symplectomorphism group…

We determine conditions under which two Hamiltonian torus actions on a symplectic manifold $M$ are homotopic by a family of Hamiltonian torus actions, when $M$ is a toric manifold and when $M$ is a coadjoint orbit.

Looijenga recently proved that the tautological ring of M_g vanishes in degree d>g-2 and is at most one-dimensional in degree g-2, generated by the class of the hyperelliptic locus. Here we show that K_{g-2} is non-zero on M_g. The proof…

Let $M$ be a closed connected smooth manifold and $G=\textmd{Diff}_0(M)$ denote the connected component of the diffeomorphism group of $M$ containing the identity. The natural action of $G$ on $M$ induces the trace homomorphism on homology.…

Recall that an effective circle action is semifree if the stabilizer subgroup of each point is connected. We show that if $(M, \om)$ is a coadjoint orbit of a compact Lie group $G$ then every element of $\pi_1(G)$ may be represented by a…

Let G be a torus of dimension n > 1 and M a compact Hamiltonian G-manifold with $M^G$ finite. A circle, $S^1$, in G is generic if $M^G = M^{S^1}$. For such a circle the moment map associated with its action on M is a perfect Morse function.…

A gap in the proof of the main result in reference [1] in our original submission propagated into the constructions presented in the first version of our manuscript. In this version we give an alternative proof for the existence of…

We prove a reduction theorem for the tangent bundle of a Poisson manifold $(M, \pi)$ endowed with a pre-Hamiltonian action of a Poisson Lie group $(G, \pi_G)$. In the special case of a Hamiltonian action of a Lie group, we are able to…

We prove the LeBrun-Salamon Conjecture in low dimensions. More precisely, we show that a contact Fano manifold X of dimension 2n+1 that has reductive automorphism group of rank at least n-2 is necessarily homogeneous. This implies that any…