Related papers: Multiplicative properties of Atiyah duality

We review and extend the theory of Thom spectra and the associated obstruction theory for orientations. We recall (from May, Quinn, and Ray) that a commutative ring spectrum A has a spectrum of units gl(A). To a map of spectra f: b ->…

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth,…

Stasheff's $A(\infty)$-algebra $(M,\{m_i:\otimes^iM\to M, i=1,2,3,...\})$ in fact is a DG-algebra $(M,m_1,m_2)$ with not necessarily associative product $m_2$ but this nonassociativity is measured by higher homotopies $m_{i>2}$.…

The topological Hochschild homology $THH(A)$ of an orthogonal ring spectrum $A$ can be defined by evaluating the cyclic bar construction on $A$ or by applying B\"okstedt's original definition of $THH$ to $A$. In this paper, we construct a…

Let $X$ be a finite CW complex, and let $DX$ be its dual in the category of spectra. We demonstrate that the Poincar\'e/Koszul duality between $THH(DX)$ and the free loop space $\Sigma^\infty_+ LX$ is in fact a genuinely $S^1$-equivariant…

For a Lie algebroid pair $A\hookrightarrow L$ we study cocycles constructed from the extension to $L$ of the higher connection forms of a representation up to homotopy $E$ of the Lie algebroid $A$. We show that there exists a cohomology…

We show the topological Hochschild homology spectrum of a twisted group algebra $\THH(A^{\tau}[G])$ is the Thom spectrum associated to a parametrized orthogonal spectrum $E(A,G)$. We then analyze the structure of the parametrized orthogonal…

In this paper, we import the theory of "Calabi-Yau" algebras and categories from symplectic topology and topological field theories to the setting of spectra in stable homotopy theory. Twistings in this theory will be particularly…

The MHV scattering amplitudes in planar N=4 SYM are dual to bosonic light-like Wilson loops. We explore various proposals for extending this duality to generic non-MHV amplitudes. The corresponding dual object should have the same…

The structure space S(M) of a closed topological m-manifold M classifies bundles whose fibers are closed m-manifolds equipped with a homotopy equivalence to M. We construct a highly connected map from S(M) to a concoction of algebraic…

Let M be a closed orientable Seifert fibered 3-manifold with a hyperbolic base 2-orbifold, or equivalently, admitting a geometry modeled on H^2 \times R or the universal cover of SL(2,R). Our main result is that the connected component of…

Given a closed monotone symplectic manifold $M$, we define certain characteristic cohomology classes of the free loop space $L \text {Ham}(M, \omega)$ with values in $QH_* (M)$, and their $S^1$ equivariant version. These classes generalize…

We show that the vector bundle on the moduli stack $M_\mathrm{ell}$ of elliptic curves associated to the $2$-cell complex $C\nu$ is isomorphic to the de Rham cohomology sheaf $\mathrm{H}^1_\mathrm{dR}(\mathcal{E}/M_\mathrm{ell})$ of the…

Given $f: M \to N$ a homotopy equivalence of compact manifolds with boundary, we use a construction of Geoghegan and Nicas to define its Reidemeister trace $[T] \in \pi_1^{st}(\mathcal{L} N, N)$. We realize the Goresky-Hingston coproduct as…

Let $f \colon R \to B$ be a surjective homomorphism of rings with kernel $I$. Gulliksen (when $I$ is generated by a regular sequence) and later Mehta (in general) showed that for any $B$-modules $M$ and $N$, $\mathrm{Ext}_B^{\ast}(M,N)$ has…

The singular set of a generic map $f: M\to F$ of a manifold $M$ of dimension $m\ge 2$ to an oriented surface $F$ is a closed smooth curve $\Sigma(f)$. We study the parity of the number of components of $\Sigma(f)$. The image $f(\Sigma)$ of…

In this article we consider algebraic structures on the homology of the space of paths in a manifold with endpoints in a submanifold. The Pontryagin-Chas-Sullivan product on the homology of this space had already been investigated by…

In this work, the set of quasi-primary ideals of a commutative ring with identity is equipped with a topology and is called quasi-primary spectrum. Some topological properties of this space are examined. Further, a sheaf of rings on the…

We prove an orbifold type decomposition theorem for the Hochschild homology of the symmetric powers of a small DG category $\mathcal{A}$. In noncommutative geometry, these can be viewed as the noncommutative symmetric quotient stacks of…

We investigate the quantum spectrum and Gamma structure for projective bundles, blow-ups, and standard flips. After restricting the quantum multiplication to the exceptional curve direction, we obtain a decomposition of the quantum…