Related papers: Weinstein Homotopies
In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…
Generalizing the theory of parity sheaves on complex algebraic stacks due to Juteau-Mautner-Williamson, we develop a theory of twisted equivariant parity sheaves. We use this formalism to construct a modular incarnation of Lusztig and Yun's…
In this paper, we establish a general relationship between the nonvanishing of GW invariants with the existence of the closed orbits of a Hamiltonian system. As an application, we completely solved the stabilized Weinstein conjecture.
We announce some results towards the classification of partially hyperbolic diffeomorphisms on 3-manifolds, and outline the proofs in the case when the diffeomorphism is dynamically coherent. Detailed proofs are long and technical and will…
We are pleased to see that Jeckelmann has made many changes to the original version of his comment on our paper as a result of our response. Here is a copy of this powerful response that reveals problems in his previous results. However,…
In this note we review some aspects of topological censorship. We present several (actually five) alternative sets of hypotheses which allow the proof of a topological censorship theorem for spacetimes with conformal completions at infinity…
This paper presents a few remarks about the topology of symplectic hyperplane sections and the geometry of their complements. In particular, it contains a detailed proof of the following result already stated with hints in [Gi]: for…
We give an proof on the Weinstein conjecture on the cotangent bundles of open manifolds. Its proof is based on Gromov's nonlinear Fredholm alternative.
We consider contact foliations: objects which generalise to higher dimensions the flow of the Reeb vector field on contact manifolds. We list a number of properties of such foliations, and propose two conjectures about the topological types…
I reply to Professor Peter van Nieuwenhuizen in connection with hep-th/0408137
A gap in a paper of Rubinstein-Scharlemann is explored: new examples are found of closed orientable 3-manifolds with possibly multiple genus 2 Heegaard splittings. Properties common to all the examples in the original paper are not…
We investigate Whitehead's asphericity question from a new perspective, using results and techniques of the homotopy theory of finite topological spaces. We also introduce a method of reduction to investigate asphericity based on the…
We give a condition for an almost constant-type manifold to be a constant-type manifold, and holomorphic and $R$-invariant submanifolds of almost Hermitian manifolds are studied. Generalizations of some results in [5] are given.
We extend the notion of a partial cohomology group $H^n(G,A)$ to the case of non-unital $A$ and find interpretations of $H^1(G,A)$ and $H^2(G,A)$ in the theory of extensions of semilattices of abelian groups by groups.
The purpose of these notes is to give a categorical presentation/analysis of homotopy type theory. The notes are incomplete as they stand (October 2017). The chapter on univalent tribes is missing. The references are not always connected to…
We give a survey of recent results, due mainly to the authors, concerning Bernstein-Markov type inequalities and connections with potential theory.
A K-theoretic counterpart of quantum cohomology theory is discussed.
Contribution to the volume "In Memory of Steven Weinberg" to appear in Nuclear Physics B.
We build free, bigraded bidifferential algebra models for the forms on a complex manifold, with respect to a strong notion of quasi-isomorphism and compatible with the conjugation symmetry. This answers a question of Sullivan. The resulting…
We obtain some new inequalities of Chebyshev Type.