相关论文: The Lusternik-Schnirelmann Category of Sp(3)

Certain solvable extensions of $H$-type groups provide noncompact counterexamples to the so-called Lichnerowicz conjecture, which asserted that ``harmonic'' Riemannian spaces must be rank 1 symmetric spaces.

In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order $v$, where $v=3^k$, and $3$-rank $v-k$. We develop an…

In this article, we construct a $2$-category of Lagrangians in a fixed shifted symplectic derived stack S. The objects and morphisms are all given by Lagrangians living on various fiber products. A special case of this gives a $2$-category…

We give three necessary and sufficient conditions for a pro-p group to be p-adic analytic. We show that a noetherian pro-p group having finite chain length has a finite rank and conversely. We further deduce that a noetherian pro-p group…

We describe the (minimal) tree-graded structure of asymptotic cones of non-geometric graph manifold groups, and as a consequence we show that all said asymptotic cones are bilipschitz equivalent. Combining this with geometrization and other…

We extend the work in a previous paper with David Li-Bland (arXiv:1401.7302) to construct the Wehrheim-Woodward category WW($G\mathbf{SLREL}$) of equivariant linear canonical relations between linear symplectic $G$-spaces for a compact…

Let $M$ be an analytic complete finite volume pseudo-Riemannian manifold and $\widetilde{Sp}(n,\mathbb{R})\times\widetilde{Sp}(1,\mathbb{R})$ a connected semisimple Lie group such that its Lie algebra is…

We extend the $sl(3)$-polynomial invariant for links to tangles. Motivated by Kuperberg's construction of this invariant via planar trivalent graphs, we first define a category of $sl(3)$ webs and its sister linear category, and describe…

We study the group of homotopy classes of self maps of compact Lie groups which induce the trivial homomorphism on homotopy groups. We completely determine the groups for SU(3) and Sp(2). We investigate these groups for simple Lie groups in…

We show that the dynamical group of an electron in a constant magnetic field is the group of symplectomorphisms $Sp(4,\mathbb{R})$. It is generated by the spinorial realization of the conformal algebra $\mathfrak{so}(2,3)$ considered in…

Kreck's modified surgery theory reduces the classification of closed, connected 4-manifolds, up to connect sum with some number of copies of $S^2\times S^2$, to a series of bordism questions. We implement this in the case of unorientable…

We define a family of link concordance invariants $\left\{ s_n \right\}_{n=2,3, \cdots}$. These link concordance invariants give lower bounds on the slice genus of a link $L$. We compute the slice genus of positive links. Moreover, these…

We characterize numerical semigroups $S$ with embedding dimension three attaining equality in the inequality $\max\Delta(S)+2\leq \operatorname{cat}(S)$, where $\Delta(S)$ denotes the Delta set of $S$ and $\operatorname{cat}(S)$ denotes the…

The determination of scalars involved in Lusztig's conjecture for finite reductive groups $G(F_q)$ was achieved by Waldspurger in the case of symplectic groups or orthogonal groups, under the condition that $p,q$ are large enough. Here $p$…

We derive the potential modular symmetries of heterotic string theory. For a toroidal compactification with Wilson line modulus, we obtain the Siegel modular group $\mathrm{Sp}(4,\mathbb{Z})$ that includes the modular symmetries…

This paper adresses the question whether the $LS$-sequences constructed by Carbone yield indeed a new family of low discrepancy sequences. While it is well known that the case $S=0$ corresponds to van der Corput sequences, we prove here…

Given two symmetric convex bodies $L \subseteq K \subseteq \R^n$ with $L$ strictly convex, we prove that there exist at least $n$ hyperplanes $H$ tangent to $L$, such that the center of mass of $H \cap K$ belongs to $\partial L$. The…

It follows from a theorem of Gromov that the stable systolic category of a closed manifold is bounded from below by the rational cup-length of the manifold. In the paper we study the inequality in the opposite direction. In particular,…

We prove a weak version of Lusztig's conjecture on explicit description of the asymptotic Hecke algebras (both finite and affine), and explain its relation to Lusztig's classification of character sheaves.

From the cohomological point of view the symplectomorphism group $Sympl (M)$ of a symplectic manifold is `` tamer'' than the diffeomorphism group. The existence of invariant polynomials in the Lie algebra $\frak {sympl }(M)$, the symplectic…