Related papers: Topological modular forms with level structure
Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been…
We present a new flavor of TAF-type (co)homology theories, which are p-local of height two and based on the isometry group of the odd unimodular hermitian lattice of signature (1,1) over the Gaussian integers. Using a suitable family of…
The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on…
The relationship between comodules of a coring and flat connections is reviewed. In particular we specialise to corings which are built on a tensor product of algebra and a coalgebra. Such corings are in one-to-one correspondence with…
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge…
We define a Hopf cyclic (co)homology theory in an arbitrary symmetric strict monoidal category. Thus we unify all different types of Hopf cyclic (co)homologies under one single universal theory. We recover Hopf cyclic (co)homology of module…
We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of the notion…
This is the companion article to the Bourbaki talk of the same name given in March 2009. The main theme of the talk and the article is to explain the interplay between homotopy theory and algebraic geometry through the Hopkins-Miller-Lurie…
We describe the quantum cohomology ring of a toric Fano variety $X$ in terms of the usual topological cohomology ring for an auxiliary infinite-dimensional scheme. This scheme is a part of an algebro-geometric model for the universal cover…
For any space X with the homotopy type of simply-connected, finite-type CW-complex, we construct an associative cochain algebra fls(X) whose cohomology algebra is isomorphic to that of LX, the free loop space on X. For certain X, we define…
Let A be an A_\infty ring spectrum. We use the description from [2] of the cyclic bar and cobar construction to give a direct definition of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another…
We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds. The…
Let $H$ be a finite-dimensional connected Hopf algebra over an algebraically closed field $\field$ of characteristic $p>0$. We provide the algebra structure of the associated graded Hopf algebra $\gr H$. Then, we study the case when $H$ is…
Topological quivers are generalizations of directed graphs in which the sets of vertices and edges are locally compact Hausdorff spaces. Associated to such a topological quiver Q is a C*-correspondence, and from this correspondence one may…
The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally…
We show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the…
We extend the Cohen-Jones-Segal construction of stable homotopy types associated to flow categories of Morse-Smale functions $f$ to the setting where $f$ is equivariant under a finite group action and is Morse but no longer Morse-Smale.…
We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…
We determine the image of the 2-primary tmf-Hurewicz homomorphism, where tmf is the spectrum of topological modular forms. We do this by lifting elements of tmf_* to the homotopy groups of the generalized Moore spectrum M(8,v_1^8) using a…