Anton Alekseev, Eckhard Meinrenken, Chris Woodward
We derive Verlinde's formula from the fixed point formula for loop groups proved in the companion paper "A fixed point formula for loop group actions", and extend it to compact, connected groups that are not necessarily simply-connected.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In 1999, Fuchs and Schweigert proposed formulas of Verlinde type for moduli spaces of surface group representations in compact nonsimply connected Lie groups. In this paper, we will prove a symplectic version of their conjecture for surfaces with at most one boundary component. A key tool in our computations is Kostant's notion of a maximal torus in apposition.
We study several questions on the existence of negative Sasakian structures on simply connected rational homology spheres and on Smale-Barden manifolds of the form $\#_k(S^2\times S^3)$. First, we prove that any simply connected rational homology sphere admitting positive Sasakian structures also admits a negative one. This result answers the question, posed by Boyer and Galicki in their book [BG], of determining which simply connected rational homology spheres admit both negative and positive Sasakian structures. Second, we prove that the connected sum $\#_k(S^2\times S^3)$ admits negative qu…
In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along $T^4$. Using our construction, we also produce symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group $\Z$. In this paper, we also produce the first examples of simply connected symplectic Calabi-Yau and non-Calabi-Yau 6-manifolds via coisotropic Luttinger surgery.
We construct a simply connected compact manifold which has complex and symplectic structures but does not admit Kähler metrics, in the lowest possible dimension where this can happen, that is, dimension 6. Such a manifold is automatically formal and has even odd-degree Betti numbers but it does not satisfy the Lefschetz property for any symplectic form.
In simply-connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms
该研究在单连通余切丛中证明了精确拉格朗日cobordism与h-cobordism之间的等价关系，利用阿布扎伊德-克拉格定理实现了基础代数拓扑学的结论。
In this paper we construct a simply connected, minimal, complex surface of general type with p_g=0 and K^2=2 using a rational blow-down surgery and Q-Gorenstein smoothing theory.
We give a complete classification of left invariant para-Kähler structures on four-dimensional simply connected Lie groups up to an automorphism. As an application we discuss some curvatures properties of the canonical connection associated to these structures as flat, Ricci flat and existence of Ricci solitons.
Motivated by a recent result of Y. Lee and the second author[7], we construct a simply connected minimal complex surface of general type with p_g=0 and K^2=3 using a rational blow-down surgery and Q-Gorenstein smoothing theory. In a similar fashion, we also construct a new simply connected symplectic 4-manifold with b_2^+=1 and K^2=4.
Examples of nonformal simply connected symplectic manifolds are constructed.
For any $N \geq 5$ nonformal simply connected symplectic manifolds of dimension $2N$ are constructed. This disproves the formality conjecture for simply connected symplectic manifolds which was introduced by Lupton and Oprea.
A non-formal simply connected compact symplectic manifold of dimension 8 is constructed.
Vidussi was the first to construct knotted Lagrangian tori in simply connected four dimensional manifolds. Fintushel and Stern introduced a second way to detect such knotting.This note demonstrates that similar examples may be distinguished by the fundamental group of the exterior.
We prove that for any number $r$ in $[2,3]$, there are spin (resp. non-spin minimal) simply connected complex surfaces of general type $X$ with $c_1^2(X)/c_2(X)$ arbitrarily close to $r$. In particular, this shows the existence of simply connected surfaces of general type arbitrarily close to the Bogomolov-Miyaoka-Yau line. In addition, we prove that for any $r \in [1,3]$ and any integer $q\geq 0$, there are minimal complex surfaces of general type $X$ with $c_1^2(X)/c_2(X)$ arbitrarily close to $r$, and $π_1(X)$ isomorphic to the fundamental group of a compact Riemann surface of genus $q$.
We show that the Craighero-Gattazzo surface, the minimal resolution of an explicit complex quintic surface with four elliptic singularities, is simply-connected. This was conjectured by Dolgachev and Werner, who proved that its fundamental group has a trivial profinite completion. The Craighero-Gattazzo surface is the only explicit example of a smooth simply-connected complex surface of geometric genus zero with ample canonical class. We hope that our method will find other applications: to prove a topological fact about a complex surface we use an algebraic reduction mod p technique and defor…
We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author. We also construct, for any group G satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic surface whose complement has fundamental group G. In each case, we produce infinitely many smoothly inequivalent surfaces that are equivalent up to smooth s-cobordism and hence are topologically equivalent for good groups.
In this paper we construct non-simply connected contact manifolds $M$ of dimension $\geq5$ such that $M\times S^1$ does not admit a symplectic structure.
We prove the existence of $(20-2K^2)$-dimensional families of simply-connected surfaces with ample canonical class, $p_g=1$, and $1 \leq K^2 \leq 9$, and we study the relation with configurations of rational curves in K3 surfaces via $\mathbb Q$-Gorenstein smoothings. Our surfaces with $K^2=7$ and $K^2=9$ are the first surfaces known in the literature, together with the existence of a $4$-dimensional family for $K^2=8$.
For each pair $(e,σ)$ of integers satisfying $2e+3σ\ge 0$, $σ\leq -2$, and $e+σ\equiv 0\pmod{4}$, with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic $e$ and signature $σ$. We also produce simply connected, minimal symplectic 4-manifolds with signature zero (resp. signature -1) with Euler characteristic $4k$ (resp. $4k+1$) for all $k\ge 46$ (resp. $k\ge 49$).
We describe a map from the equivariant twisted K-homology of a compact, connected, simply connected Lie group $G$ to the Verlinde ring. Our map is described at the level of `D-cycles' for the geometric twisted K-homology of $G$, and is inverse to the Freed-Hopkins-Teleman isomorphism. As an application, we show that two possible definitions of the `quantization' of a Hamiltonian loop group space are compatible with each other.
In this article we construct a new family of simply connected symplectic 4-manifolds with $b_2^+ =1$ and $c_1^2 =2$ which are not diffeomorphic to rational surfaces by using rational blow-down technique. As a corollary, we conclude that a rational surface ${\mathbf CP}^2 \sharp 7{\bar{\mathbf CP}^2}$ admits an exotic smooth structure.
We prove results exploring the relationship between the fundamental group and the second Betti number of minimal symplectic fillings of lens spaces. These results unify and generalize several disparate facts appearing in the literature. The Fibonacci numbers make a cameo appearance.
We show an alternative construction of the first example of a simply-connected compact symplectic non-formal 8-manifold given in arXiv:math/0506449. We also give an alternative proof of its non-formality using higher order Massey products.
We prove that any closed simply-connected smooth 4-manifold is 16-fold branched covered by a product of an orientable surface with the 2-torus, where the construction is natural with respect to spin structures. In particular this solves Problem 4.113(C) in Kirby's list. We also discuss analogous results for other families of 4-manifolds with infinite fundamental groups.
For 5 <= k <= 8 we show that the infinite family of exotic smooth structures on CP^2# k(-CP^2) can be achieved by 1/n - surgeries on a single embedded nullhomologous torus in a manifold R_k which is homeomorphic to CP^2# k(-CP^2).
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。