Related papers: The Becker-Gottlieb Transfer Is Functorial
We show that any homotopy Gerstenhaber algebra is naturally a strongly homotopy commutative (shc) algebra in the sense of Stasheff-Halperin with a homotopy associative structure map. In the presence of certain additional operations…
We show that a map between fibrant objects in a closed model category is a weak equivalence if and only if it has the right homotopy extension lifting property with respect to all cofibrations. The dual statement holds for maps between…
For a proper map $f\colon X\to Y$ of noetherian ordinary schemes, one has a well-known natural transformation, ${\bf L}^*f^*(-)\overset{\bf L}{\otimes} f^!{\mathcal{O}}_Y\to f^!$, obtained via the projection formula, which extends, using…
Building on the 10-way symmetry classification of disordered fermions, the authors have recently given a homotopy-theoretic proof of Kitaev's "Periodic Table" for topological insulators and superconductors. The present paper offers an…
Let k be an algebraically closed field of characteristic 0, and let f be a morphism of smooth projective varieties from X to Y over the ring k((t)) of formal Laurent series. We prove that if a general geometric fiber of f is rationally…
Functor morphing provides a method to translate complex representations of automorphism groups of finite modules over finite rings to representations of automorphism groups of functors in some abelian category. In this paper we give an…
Discrete homotopy theory or A-homotopy theory is a combinatorial homotopy theory defined on graphs, simplicial complexes, and metric spaces, reflecting information about their connectivity. The present paper aims to further understand the…
An elementary notion of homotopy can be introduced between arrows in a cartesian closed category $E$. The input is a finite-product-preserving endofunctor $\Pi_0$ with a natural transformation $p$ from the identity which is surjective on…
We consider algebras defined over a complete, local and noetherian ground ring. They are gentle algebras in case the ground ring is a field. The unbounded homotopy category of complexes of projective modules is considered. Complexes with…
We develop a theory of generalized characters of local systems in $\infty$-categories, which extends classical character theory for group representations and, in particular, the induced character formula. A key aspect of our approach is…
For a (right and left) coherent ring $A$, we show that there exists a duality between homotopy categories ${\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A^{{\rm op}})$ and ${\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A)$. If $A=\Lambda$ is an…
We construct a small realization as flow of every precubical set (modeling for example a process algebra). The realization is small in the sense that the construction does not make use of any cofibrant replacement functor and of any…
We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors…
We establish an upper bound for the cochain type level of the total space of a pull-back fibration. It explains to us why the numerical invariant for a principal bundle over the sphere are less than or equal to two. Moreover computational…
For a complex projective manifold, Walker has defined a regular homomorphism lifting Griffiths' Abel-Jacobi map on algebraically trivial cycle classes to a complex abelian variety, which admits a finite homomorphism to the Griffiths…
We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this…
We study elements of the spectral theory of compact hyperbolic orbifolds $\Gamma \backslash \mathbb{H}^{n}$. We establish a version of the Selberg trace formula for non-unitary representations of $\Gamma$ and prove that the associated…
The analogy between Yetter's deformation theory form (lax) monoidal functors and Gerstenahaber's deformation theory for associative algebras is solidified by shown that under reasonable conditions the category of functors with an action of…
We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize…
Cubical type theories are designed around an abstract unit interval from which types of paths, used to represent equalities, are defined. Varying the operations available on this interval yields different type theories. A reversal is an…