## 118 Citations

### THE GEOMETRY OF THE LOCAL COHOMOLOGY FILTRATION IN EQUIVARIANT BORDISM

- Mathematics
- 2001

We present geometric constructions which realize the local cohomology Þltration in the setting of equivariant bordism, with the aim of understanding free G actions on manifolds. We begin by reviewing…

### Geometric versus homotopy theoretic equivariant bordism

- Mathematics
- 2004

By results of Löffler and Comezaña, the Pontrjagin-Thom map from geometric G-equivariant bordism to homotopy theoretic equivariant bordism is injective for compact abelian G. If G=S1×⋯×S1, we prove…

### Equivariant cohomology and the super reciprocal plane of a hyperplane arrangement

- MathematicsAlgebraic & Geometric Topology
- 2022

In this paper, we investigate certain graded-commutative rings which are related to the reciprocal plane compactification of the coordinate ring of a complement of a hyperplane arrangement. We give a…

### Equivariant orientations and $G$-bordism theory.

- Mathematics
- 1989

We outline a new geometric theory of orientations under the action of a group G and formulate bordism theories for (7-oriented manifolds. These theories extend the classical G-bordism theories…

### Transversality Obstructions and Equivariant Bordism for G=Z/2

- Mathematics
- 1999

In this paper we compute homotopical equivariant bordism for the group ${\bf Z/2}$, namely $MO^{\bf Z/2}$, geometric equivariant bordism $\Omega^{\bf Z/2}_*$, and their quotient as modules over…

### Witt Vectors and Equivariant Ring Spectra

- Mathematics
- 2004

This paper establishes a connection between equivariant ring spectra and Witt vectors in the sense of Dress and Siebeneicher. Given a commutative ringspectrum T in the highly structured sense, that…

### On the Equivariant Lazard Ring and Tom Dieck's Equivariant Cobordism Ring

- Mathematics
- 2013

For a torus G of rank r = 1, we showed that the canonical ring homomorphism L_G \to MU_G, where L_G is the equivariant Lazard ring and MU_G is the equivariant cobordism ring introduced by Tom Dieck,…

### Equivariant Algebraic Cobordism and Equivariant Formal Group Laws

- Mathematics
- 2013

We introduce an equivariant algebraic cobordism theory \Omega^G for algebraic varieties with G-action, where G is a split diagonalizable group scheme over a field k. It is done by combining the…

### Equivariant $K$-theory of toric orbifolds

- Mathematics
- 2021

Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric…

## References

SHOWING 1-10 OF 35 REFERENCES

### Differentiable periodic maps

- Mathematics
- 1964

1. The bordism groups. This note presents an outline of the authors' efforts to apply Thorn's cobordism theory [ó] to the study of differentiable periodic maps. First, however, we shall outline our…

### Equivariant K-theory

- Mathematics
- 1968

The purpose of this thesis is to present a fairly complete account of equivariant K-theory on compact spaces. Equivariant K-theory is a generalisation of K-theory, a rather well-known cohomology…

### Equivariant cohomology theories

- Mathematics
- 1967

Throughout this note G denotes a discrete group. A G-complex is a CPP-complex on which G acts by cellular maps such that the fixed point set of any element of G is a subcomplex. On the category of…

### The relation of cobordism to k-theories

- History
- 1966

• November 2nd, 2006: Talk 1 by Marc Siegmund: This should be an introduction to bordism, tell us the geometric constructions and mention the ring structure of Ω ∗ . You might take the books of…

### Stable Homotopy Theory

- Mathematics
- 1969

There is a number of phenomena in homotopy theory which are independent of the precise dimensions considered, provided that the dimensions are large enough. For example, nn+1(Sn) = Z2 for n > 2. Such…

### The representation ring of a compact Lie group

- Mathematics
- 1968

© Publications mathématiques de l’I.H.É.S., 1968, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…

### FaserbÜndel mit Gruppenoperation

- Mathematics
- 1969

(Wir nehmen wie fiblich an, dab G yon reehts auf E operiert.) Wir bezeichnen ein (F, ~, G)-Bfindel meist nut dnreh die zugrunde liegende Abbildung p: E --> B. Ist trivial, dann operiert F als Gruppe…