LetM be a closed, connected, orientable topological four-manifold with H1(M) nontrivial and free abelian, b2(M) 6= 0, 2, and χ(M) 6= 0. Then the only finite groups which admit homologically trivial, locally linear, effective actions on M are cyclic. The proof uses equivariant cohomology, localization, and a careful study of the first cohomology groups of the (potential) singular set.

Goresky, Kottwitz and MacPherson have recently shown that the computation of the equivariant cohomology ring of a G-manifold can be reduced to a computation in graph theory. This opens up the possibility that many of the fundamental theorems in equivariant de Rham theory may, on closer inspection, turn out simply to be theorems about graphs. In this paper we show that for some familiar theorems...

A torus manifold is an even-dimensional manifold acted on by a half-dimensional torus with non-empty fixed point set and some additional orientation data. It may be considered as a far-going generalisation of toric manifolds from algebraic geometry. The orbit space of a torus manifold has a reach combinatorial structure, e.g., it is a manifold with corners provided that the action is locally st...

We identify the equivariant structure of filtered pieces motivic filtration defined by Bhatt, Morrow and Scholze on topological Hochschild cohomology spectrum polynomial algebras over Fp.

The classical Pieri formula is an explicit rule for determining the coefficients in the expansion s1m · sλ = ∑ c 1,λ sμ , where sν is the Schur polynomial indexed by the partition ν. Since the Schur polynomials represent Schubert classes in the cohomology of the complex Grassmannian, this gives a partial description of the cup product in this cohomology. Pieri’s formula was generalized to the c...

Abstract We study the Demazure–Lusztig operators induced by left multiplication on partial flag manifolds $G/P$. prove that they generate Chern–Schwartz–MacPherson classes of Schubert cells (in equivariant cohomology), respectively their motivic Chern K-theory), in any manifold. Along way, we advertise many properties and right divided difference cohomology K-theory actions classes. apply this ...

Schubert polynomials, which a priori represent cohomology classes of Schubert varieties in the flag manifold, also represent torus-equivariant cohomology classes of certain determinantal loci in the vector space of n×n complex matrices. Our central result is that the minors defining these “matrix Schubert varieties” are Gröbner bases for any antidiagonal term order. The Schubert polynomials are...

Schubert polynomials, which a priori represent cohomology classes of Schubert varieties in the flag manifold, also represent torus-equivariant cohomology classes of certain determinantal loci in the vector space of n×n complex matrices. Our central result is that the minors defining these “matrix Schubert varieties” are Gröbner bases for any antidiagonal term order. The Schubert polynomials are...

We describe the cohomology ring of the symplectic reductions by tori of coadjoint orbits, or weight varieties. Weight varieties arise from representation theory considerations, and are temed as such because they are the symplectic analogue of the T-isotypic components (weight spaces) of irreducible representations of G. Recently, Tolman and Weitsman expressed the (ordinary) cohomology ring for ...