相关论文: The universal functorial equivariant Lefschetz inv…

We study the category of $\mathbf{P}$-equivariant modules over the infinite variable polynomial ring, where $\mathbf{P}$ denotes the subgroup of the infinite general linear group $\mathbf{GL}(\mathbf{C}^\infty)$ consisting of elements…

Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear…

Let $K$ be an algebraically closed field. Let $G$ be a non-trivial connected unipotent group, which acts effectively on an affine variety $X.$ Then every non-empty component $R$ of the set of fixed points of $G$ is a $K$-uniruled variety,…

We characterize the irreducible polynomials that occur as a characteristic polynomial of an automorphism of an even unimodular lattice of given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general…

We construct a 2-category version of tom Dieck's equivariant fundamental groupoid for representable orbifolds and show that the discrete fundamental groupoid is Morita invariant; hence an orbifold invariant for representable orbifolds.

We prove an equivariant Lefschetz formula for elliptic complexes over a compact manifold carrying the action of a compact Lie group of isometries via heat equation methods.

In this paper we propose a new treatment about infinite dimensional manifolds, using the language of category and functor. Our definition of infinite dimensional manifolds is a natural generalization of finite dimensional manifolds in the…

We present a decomposition of rational twisted $G$-equivariant K-theory, $G$ a finite group, into cyclic group equivariant K-theory groups of fixed point spaces. This generalises the untwisted decomposition by Atiyah and Segal as well as…

Let $G$ be a finite group, and $C$ be an abelian group. We introduce the notions of $C$-monomial $G$-sets and $C$-monomial $G$-posets, and state some of their categorical properties. This gives in particular a new description of the…

We prove two general factorization theorems for fixed-point invariants of fibrations: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar multiplicativity results for the Lefschetz and Nielsen…

A theorem of Gerald Schwarz [24, Thm. 1] says that for a linear action of a compact Lie group $G$ on a finite dimensional real vector space $V$ any smooth $G$-invariant function on $V$ can be written as a composite with the Hilbert map. We…

Consider a Hamiltonian action of a compact Lie group on a symplectic manifold which has the strong Lefschetz property. We establish an equivariant version of the Merkulov-Guillemin $d\delta$-lemma and an improved version of the…

An interpretation of the Casselman-Wallach (C-W) Theorem is that the $K$-finite functor is an isomorphism of categories from the category of finitely generated, admissible smooth Fr\'echet modules of moderate growth to the category of…

Let $X$ be a CR manifold with transversal, proper CR $G$-action. We show that $X/G$ is a complex space such that the quotient map is a CR map. Moreover the quotient is universal, i.e. every invariant CR map into a complex manifold…

The purpose of this paper is to prove an equivariant Riemann-Roch theorem for schemes or algebraic spaces with an action of a linear algebraic group $G$. For a $G$-space $X$, this theorem gives an isomorphism between a completion of the…

In this paper, given a finitely presented group $\Gamma$, we provide the explicit monodromy of a Lefschetz fibration with $(-1)$-sections whose total space has fundamental group $\Gamma$ by applying "twisted substitutions" to that of the…

In a pair of papers, we construct invariants for smooth four-manifolds equipped with `broken fibrations' - the singular Lefschetz fibrations of Auroux, Donaldson and Katzarkov - generalising the Donaldson-Smith invariants for Lefschetz…

In this paper we prove that a deformed tensor product of two Lefschetz algebras is a Lefschetz algebra. We then use this result in conjunction with some basic Schubert calculus to prove that the coinvariant ring of a finite reflection has…

For each subgroup of GL_2(F_p) or order divisible by p, generated by (pseudo-)reflections, we compute the ideals of stable and generalized invariants. These groups and these ideals are related to the cohomology of compact Lie groups,…

Using variational considerations, we establish that there exists a new symmetric trace-free tensor conformal invariant of hypersurfaces embeddings in even dimensional conformal manifolds. This conformal invariant completes the family of…