相关论文: An integer valued SU(3) Casson invariant

We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete…

A specific algebraic coupling model involving multiple quantization axes is presented in which previously indistinguishable SU(2) symmetry groups become distinguishable when coupled into a SU(3) group structure. The model reveals new…

We study framed links in irreducible 3-manifolds that are $Z$-homology 3-spheres or atoroidal $Q$-homology 3-spheres. We calculate the dual of the Kauffman skein module over the ring of two variable power series with complex coefficients.…

Three-manifold invariants $\hat Z$ (''$Z$-hat''), also known as homological blocks, are $q$-series with integer coefficients. Explicit $q$-series form for $\hat Z$ is known for $SU(2)$ group, supergroup $SU(2|1)$ and ortho-symplectic…

For Seifert manifold $M=X({p_1}/_{\f{q_1}},{p_2}/_{\f{q_2}}, ...,{p_n}/_ {\f{q_n}}), \tau^{'}_r(M)$ is calculated for all $r$ odd $\geq 3$. If $r$ is coprime to at least $n-2$ of $p_k$ (e.g. when $M$ is the Poincare homology sphere), it is…

We determine when the integral homology of the classifying space of a PU(n)-gauge group over the sphere S^2 has torsion.

We study Euclidean 3D N=2 supersymmetric gauge theories on squashed three-spheres preserving isometries SU(2) x U(1) or U(1) x U(1). We show that, when a suitable background U(1) gauge field is turned on, these squashed spheres support…

Gauge invariance is extended to allow to allow for a U(1)-SU(2) mixing term, which can cause a SU(2) deconfining transition.

In this article, we explore the low energy structure of a $U(3)$ gauge theory over spaces with fuzzy sphere(s) as extra dimensions. In particular, we determine the equivariant parametrization of the gauge fields, which transform either…

An approximate technique for performing nonperturbative calculations in quantum SU(3) gauge theory is presented. One aspect of this nonperturbative method is the breaking down $SU(3) \to SU(2) + coset$. The procedure also uses some aspects…

In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As application, we give a formula for the Burns-Epstein invariant, modulo an…

We study the gauge invariant cosmological perturbations up to second order. We show that there are infinite families of gauge invariant variables at both of the first and second orders. The conversion formulae among different families are…

In this paper we present our results on the homology cobordism group $\Th$ of the oriented integral homology 3-spheres. We specially emphasize the role played in the subject by the gauge theory including Floer homology and invariants by…

In this paper we achieve the quantization of a particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using group-theoretical methods. For this purpose, a fundamental role is played by contact,…

A homological invariant of 3-manifolds is defined, using abelian Yang-Mills gauge theory. It is shown that the construction, in an appropriate sense, is functorial with respect to the families of 4-dimensional cobordisms. This construction…

The complete lists of vector hyperbolic equations on the sphere that have integrable third order vector isotropic and anisotropic symmetries are presented. Several new integrable hyperbolic vector models are found. By their integrability we…

We define an invariant of triple-point-free immersions of $2$-spheres into Euclidean $3$-space, taking values in $l^1(\mathbb{Z})$. It remains unchanged under regular homotopies through such immersions. An explicit description of its image…

The f-invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; it can be formulated as an elliptic genus of manifolds with corners of codimension two. In this thesis, we develop a…

Ozsv\'ath and Szab\'o used the knot filtration on $\widehat{CF}(S^3)$ to define the $\tau$-invariant for knots in the 3-sphere. In this article, we generalize their construction and define a collection of $\tau$-invariants associated to a…

Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented $4$-manifold $X$ with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded $3$-manifold $Y$ representing a…