Related papers: The Wirthmuller isomorphism revisited

There are many contexts in algebraic geometry, algebraic topology, and homological algebra where one encounters a functor that has both a left and right adjoint, with the right adjoint being isomorphic to a shift of the left adjoint…

Let $V$ and $W$ be finite dimensional real vector spaces and let $G\subset\GL(V)$ and $H\subset\GL(W)$ be finite subgroups. Assume for simplicity that the actions contain no reflections. Let $Y$ and $Z$ denote the real algebraic varieties…

If $G$ is a finite group or a torus, it is known that there is an isomorphism between the Grothendieck group of homotopy representations and that of generalized homotopy representations for $G$. We prove that there is such an isomorphism…

We clarify the relationship between Grothendieck duality \`a la Neeman and the Wirthm\"uller isomorphism \`a la Fausk-Hu-May. We exhibit an interesting pattern of symmetry in the existence of adjoint functors between compactly generated…

In this paper we study a model structure on a category of schemes with a group action and the resulting unstable and stable equivariant motivic homotopy theories. The new model structure introduced here samples a comparison to the one by…

The hammock localization provides a model for a homotopy function complex in any Quillen model category. We prove that a homotopy between a pair of morphisms induces a homotopy between the maps induced by taking the hammock localization. We…

We construct Bott-type and stable equivariant Seiberg-Witten Floer homology and cohomology for rational homology spheres, and prove their diffeomorphism invariance.

For a rational homology 3-sphere $Y$ with a $\spinc$ structure $\s$, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology lead to a collection of variants which are topological…

We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers. In conjunction with…

An equivariant version of the twisted inverse pseudofunctor is defined, and equivariant versions of some important properties, including the Grothendieck duality of proper morphisms and flat base change are proved. As an application, a…

Let ($\mathfrak{g},\mathsf{g})$ be a pair of complex finite-dimensional simple Lie algebras whose Dynkin diagrams are related by (un)folding, with $\mathsf{g}$ being of simply-laced type. We construct a collection of ring isomorphisms…

We give rigorous foundations for parametrized homotopy theory in this monograph. After preliminaries on point-set topology, base change functors, and proper actions of non-compact Lie groups, we develop the homotopy theory of equivariant…

An isovariant map is an equivariant map between $G$-spaces which strictly preserves isotropy groups. We consider an isovariant analogue of Klein--Williams equivariant intersection theory for a finite group $G$. We prove that under certain…

We define and study equivariant periodic cyclic homology for locally compact groups. This can be viewed as a noncommutative generalization of equivariant de Rham cohomology. Although the construction resembles the Cuntz-Quillen approach to…

A theorem of L\"utkebohmert states that a rigid group homomorphism from the formal multiplicative group to a smooth commutative rigid group $G$, with relatively compact image, can be extended to a homomorphism from the rigid multiplicative…

A wide generalization of the classical theorem of A. Grothendieck asserting that for any faithfully flat extension of commutative rings, the corresponding relative Picard group and the Amitsur 1-cohomology group with values in the…

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

We apply the Acyclicity Theorem of Hess, Kerdziorek, Riehl, and Shipley (recently corrected by Garner, Kedziorek, and Riehl) to establishing the existence of model category structure on categories of coalgebras over comonads arising from…

We find lower bounds on the rank of a "real" vector bundle over an involutive space, such that "real" vector bundles of higher rank have a trivial summand and such that a stable isomorphism for such bundles implies ordinary isomorphism. We…

We present a formalism within which the relationship (discovered by Drinfel'd) between associators (for quasi-triangular quasi-Hopf algebras) and (a variant of) the Grothendieck-Teichmuller group becomes simple and natural, leading to a…