相关论文: The third homology of $\mathrm{SL}_2(\mathbb{Q})$

Let X be a space and write LX for its free loop space equipped with the action of the circle group T given by dilation. We compute the equivariant cohomology H^*(LX_hT; Z/p) as a module over H^*(BT; Z/p) when X=CP^r for any positive integer…

In this article we construct Symmetric operations for all primes (previously known only for p=2). These unstable operations are more subtle than the Landweber-Novikov operations, and encode all p-primary divisibilities of characteristic…

We compute the noncommutative de Rham cohomology for the finite-dimensional q-deformed coordinate ring $C_q[SL_2]$ at odd roots of unity and with its standard 4-dimensional differential structure. We find that $H^1$ and $H^3$ have three…

This paper studies the (small) quantum homology and cohomology of fibrations $p: P\to S^2$ whose structural group is the group of Hamiltonian symplectomorphisms of the fiber $(M,\om)$. It gives a proof that the rational cohomology splits…

Let V be a symplectic vector space of dimension 2n. Given a partition \lambda with at most n parts, there is an associated irreducible representation S_{[\lambda]}(V) of Sp(V). This representation admits a resolution by a natural complex…

We construct a functor which maps conjugate pseudo-Anosov automorphisms of a surface to the so-called stably isomorphic stationary AF-algebras; the functor gives new topological invariants of three dimensional manifolds coming from the…

In this note we present the classification of non-symplectic automorphisms of prime order on K3 surfaces, i.e.we describe the topological structure of their fixed locus and determine the invariant lattice in cohomology. We provide new…

In this paper, we compute the entire cyclic cohomology of noncommutative 3-spheres. First of all, we verify the Mayer-Vietoris exact sequence of entire cyclic cohomology in the framework of Fr\'echet $^*$-algebras. Applying it to their…

Let $G$ be a simply-connected, simple compact Lie group of type $\{n_{1},\ldots,n_{\ell}\}$, where $n_{1}\le\cdots \le n_{\ell}$. Let $\mathcal{G}_k$ be the gauge group of the principal $G$-bundle (namedright{P}{}{S^{4}}) whose isomorphism…

We study the structure of the indecomposable direct summands of tensor products of two restricted simple $SL_3(K)$-modules, where $K$ is an algebraically closed field of characteristic $p \geq 5$. We give a characteristic-free algorithm for…

We study homology and cohomology of triassociative algebras with non-trivial coefficients.

The space of realizations of a finite-dimensional Lie algebra by first order differential operators is naturally isomorphic to H^1 with coefficients in the module of functions. The condition that a realization admits a finite-dimensional…

Let g be the Lie superalgebra p(3) of rank 2 over an algebraically closed field K of characteristic p > 3. We classify all irreducible modules of g, and give the character formulae for irreducible modules.

We prove that there is an algorithm which determines whether or not a given 2-polyhedron can be embedded into some integral homology 3-sphere. This is a corollary of the following main result. Let $M$ be a compact connected orientable…

We exhibit a knot $P$ in the solid torus, representing a generator of first homology, such that for any knot $K$ in the 3-sphere, the satellite knot with pattern $P$ and companion $K$ is not smoothly slice in any homology 4-ball. As a…

It is shown in the paper that each Hecke symmetry R with the R-symmetric algebra freely generated by 3 commuting elements is determined by a bivector and a symmetric bilinear form on a 3-dimensional vector space. A general formula for such…

We determine the homological dimension of various isogeny categories of commutative algebraic groups over a field $k$, in terms of the cohomological dimension of $k$ at certain primes. This generalizes results of Serre, Oort and Milne, by…

We prove that the quantum SO(3)-invariant of an arbitrary 3-manifold $M$ is always an algebraic integer, if the order of the quantum parameter is co-prime with the order of the torsion part of $H_1(M,\BZ)$. An even stronger integrality,…

The group is interesting as the first example of split rank 2 semisimple group, all the irreducible unitary representations of which are known. We make a precise realization of the discrete series representations (in Section 2) by using the…

The trace or the $0$th Hochschild--Mitchell homology of a linear category $\mathcal{C}$ may be regarded as a kind of decategorification of $\mathcal{C}$. We compute traces of the two versions $\dot{\mathcal{U}}$ and $\dot{\mathcal{U}}^*$ of…