Related papers: Covering Homology

We consider a family of tight contact structures on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show some algebraic equivariant…

If a closed smooth manifold $M$ with an action of a torus $T$ satisfies certain conditions, then a labeled graph $\mG_M$ with labeling in $H^2(BT)$ is associated with $M$, which encodes a lot of geometrical information on $M$. For instance,…

We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to…

We apply a version of the Chas-Sullivan-Cohen-Jones product on the higher loop homology of a manifold in order to compute the homology of the spaces of continuous and holomorphic maps of the Riemann sphere into a complex projective space.…

Putman and Wieland conjectured that if $\tilde{\Sigma} \rightarrow \Sigma$ is a finite branched cover between closed oriented surfaces of sufficiently high genus, then the orbits of all nonzero elements of $H_1(\tilde{\Sigma};\mathbb{Q})$…

The integral cohomology ring of the complement of an arrangement of linear subspaces of a finite dimensional complex projective space is determined by combinatorial data, i.e. the intersection poset and the dimension function.

We define cyclic cohomology of corings over not necessarily commutative algebras. We observe that the key fact which allows us to define this complex is that enveloping algebra of an algebra is a para Hopf algebroid. This observation…

Chas and Sullivan recently defined an intersection product on the homology $H_*(LM)$ of the space of smooth loops in a closed, oriented manifold $M$. In this paper we will use the homotopy theoretic realization of this product described by…

If $X$ is a topological space then there is a natural homomorphism $\pi_1(X)\rightarrow K_1(X)$ from a fundamental group to a $K_1$-homology group. Covering projections depend of fundamental group. So $K_1$-homology groups are interrelated…

For each manifold or effective orbifold $Y$ and commutative ring $R$, we define a new homology theory $MH_*(Y;R)$, $M$-$homology$, and a new cohomology theory $MH^*(Y;R)$, $M$-$cohomology$. For $MH_*(Y;R)$ the chain complex…

The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as the distribution of galaxies in cosmology. In practice,…

In general a universal covering of a non connected topological group need not admit a topological group structure such that the covering map is a morphism of topological groups. This result is due to R.L. Taylor (1953). We generalise this…

Let $U$ be a smooth connected complex algebraic variety, and let $f\colon U\to \mathbb C^*$ be an algebraic map. To the pair $(U,f)$ one can associate an infinite cyclic cover $U^f$, and (homology) Alexander modules are defined as the…

This is a survey paper on cohomology theories for $A_\infty$ and $E_\infty$ ring spectra. Different constructions and main properties of topological Andr\'e-Quillen cohomology and of topological derivations are described. We give sample…

We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applying cyclic duality to the underlying cocyclic…

Quasiperiodic patterns described by polyhedral "atomic surfaces" and admitting matching rules are considered. It is shown that the cohomology ring of the continuous hull of such patterns is isomorphic to that of the complement of a torus…

Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology, and Bohmann-Gerhardt-H{\o}genhaven-Shipley-Ziegenhagen developed a coB\"okstedt spectral sequence to compute the homology of coTHH for…

We compute the Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners. We show in particular that the spectral sequence associated with Hochschild homology…

Let $p: S\to S_g$ be a finite covering of an orientable closed surface of genus $g$. We prove that, for $g\geq 3$, the rational homology group $H_1(S;{\mathbb Q})$ is generated by cycles supported on simple closed curves $\gamma\subset S$…

Effective homology techniques allow us to compute homology groups of a wide family of topological spaces. By the Whitehead tower method, this can also be used to compute higher homotopy groups. However, some of these techniques (in…