Related papers: On the Chern numbers for pseudo-free circle action…

We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total space of a nontrivial circle bundle over a Riemann surface). When M is a Seifert manifold, Lawrence and Rozansky have shown from the exact solution of Chern-Simons…

We give a description of the negative bundles for the energy integral on the free loop space $L{\mathbb{C}\mathrm{P}}^n$ in terms of circle vector bundles over projective Stiefel manifolds. We compute the mod $p$ Chern classes of the…

Consider a circle action on an 8-dimensional compact almost complex manifold with 4 fixed points. To the author's knowledge, $S^2 \times S^6$ is the only known example of such a manifold. In this paper, we prove that if the circle acts on…

Let $M$ be a $2n$-dimensional closed symplectic manifold admitting a Hamiltonian circle action with isolated fixed points. We show that if $M$ contains an $S^1$-invariant symplectic hypersurface $D$ such that $M\setminus D$ is a homology…

We obtain a general lower bound for the number of fixed points of a circle action on a compact almost complex manifold $M$ of dimension $2n$ with nonempty fixed point set, provided the Chern number $c_1c_{n-1}[M]$ vanishes. The proof…

% A new, formal, non-combinatorial approach to invariants of % three-dimensional manifolds of Reshetikhin, Turaev and % Witten in the framework of non-perturbative topological % quantum Chern-Simons theory, corresponding to an arbitrary %…

We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become…

Using the Dirac and the Yang monopole in spinor condensates as examples, we show that interactions can stretch the point singularity of a monopole into an extended manifold, whose shape is strongly influenced by the sign of interaction. The…

We construct Chern-Weil classes on infinite dimensional vector bundles with structure group contained in the algebra $\cl[\leq 0](M, E)$ of non-positive order classical pseudo-differential operators acting on a finite rank vector bundle $E$…

Consider an effective Hamiltonian circle action on a compact symplectic $2n$-dimensional manifold $(M, \omega)$. Assume that the fixed set $M^{S^1}$ is {\em minimal}, in two senses: it has exactly two components, $X$ and $Y$, and $\dim(X) +…

Building on the covariant supergraph techniques in 4D N = 2 harmonic superspace, we develop a manifestly 5D N = 1 supersymmetric and gauge covariant formalism to compute the one-loop effective action for a hypermultiplet coupled to a…

We study complex Chern-Simons theory on a Seifert manifold $M_3$ by embedding it into string theory. We show that complex Chern-Simons theory on $M_3$ is equivalent to a topologically twisted supersymmetric theory and its partition function…

The role of Chern-Simons (CS) actions is reviewed, starting from the observation that all classical actions in Hamiltonian form can be viewed as 0+1 CS systems, in the same class with the coupling between the electromagnetic field and a…

We define a sequence of invariants $\mathcal{Z}_{N}^{\psi}$ of tangles with flat $\mathfrak{sl}_{2}$ connections (i.e. hyperbolic structures) on their complements. These can be interpreted as a geometric twist of the Kashaev invariant or as…

In this note, we give a short proof of the localization formula for the loop space Chern character of a compact Riemannian spin manifold M, using the rescaled spinor bundle on the tangent groupoid associated to M.

We compute the Chern-Connes character (a map from the $K$-theory of a C$^*$-algebra under the action of a Lie group to the cohomology of its Lie algebra) for the $L^2$-norm closure of the algebra of all classical zero-order…

We provide an explicit computation of the cohomology groups (with untwisted coefficients) of semidirect products of the form $\mathbb{Z}^n\rtimes \mathbb{Z}/m$ with $m$ free of squares, by means of formulas that only depend on $n$, $m$ and…

In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable $C^*$-algebra by a twisted $\mathbb{R}^d$-action. The…

For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading free energy is given by F_{1}(S)=\pm{1/4}\frac{\del F_{0}(S)}{\del S}. Motivated by the fact that this relationship does not hold for Chern-Simons theory on S^{3},…

Libgober and Wood proved that the Chern number $c_{1}c_{n-1}$ of a $n$-dimensional compact complex manifold can be determined by its Hirzebruch $\chi_{y}$-genus. Inspired by the idea of their proof, we show that, for compact, spin,…