## 6 Citations

### Rank conditions for finite group actions on 4-manifolds

- MathematicsCanadian Journal of Mathematics
- 2021

Abstract Let M be a closed, connected, orientable topological
$4$
-manifold, and G be a finite group acting topologically and locally linearly on M. In this paper, we investigate the spectral…

### DUALITY IN

- Mathematics
- 2002

Let G = S 1 , G = Z/p or more generally G be a finite p-group, where p is an odd prime. If G acts on a space whose cohomology ring fulfills Poincaré duality (with appropriate coefficients k), we…

### Poincaré duality in P.A. Smith theory

- Mathematics
- 2002

Let G = S 1 , G = Z=p or more generally G be a nite p- group, where p is an odd prime. If G acts on a space whose cohomology ring fullls Poincar e duality (with appropriate coecients k), we prove a…

### On Sikora's spectral sequences

- Mathematics
- 2006

In his study of Poincare duality of a space X acted on by a group G, Sikora uses three spectral sequences which he calls the Leray, the Leray–Serre and the Swan spectral sequences. I show that, if G…

### Symmetry groups of non-simply-connected four-manifolds

- Mathematics
- 2007

Let $M$ be a closed, connected, orientable topological four-manifold with $H_1(M)$ nontrivial and free abelian, $b_2(M)\ne 0, 2$, and $\chi(M)\ne 0$. We show that if $G$ is a finite group of 2-rank…

### Do manifolds have little symmetry?

- Mathematics
- 2006

Abstract.This note surveys certain aspects (including recent results) of the following problem stated by F. Raymond and R. Schultz: “It is generally felt that a manifold ‘chosen at random’ will have…

## References

SHOWING 1-10 OF 30 REFERENCES

### Poincaré duality in P.A. Smith theory

- Mathematics
- 2002

Let G = S 1 , G = Z=p or more generally G be a nite p- group, where p is an odd prime. If G acts on a space whose cohomology ring fullls Poincar e duality (with appropriate coecients k), we prove a…

### Surgeries on periodic links and homology of periodic 3-manifolds

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2001

Fix a prime integer p. We show that a closed orientable 3-manifold M admits an action of Zp with the fixed point set S1 if and only if M can be obtained as the result of surgery on a p-periodic…

### Cohomological methods in transformation groups

- Mathematics
- 1993

Preface 1. Equivalent cohomology of G-CW-complexes and the Borel construction 2. Summary of some aspects of rational homotopy theory 3. Localisation 4. General results on torus and p-torus actions 5.…

### Actions of SO(2) on 3-Manifolds

- Mathematics
- 1968

The purpose of this report is to give a complete equivariant and topological classification of the effective actions of the circle group, SO(2), on closed, connected 3-manifolds. The equivariant…

### The Spectrum of an Equivariant Cohomology Ring: II

- Mathematics
- 1971

Let G be a compact Lie group (e.g., a finite group) and let HG= H*(BG, Z/pZ) be its mod p cohomology ring. One knows this ring is finitely generated, hence upon dividing out by the ideal of nilpotent…

### A new method in fixed point theory

- Mathematics
- 1959

EÎ'(X, A) = Ê\T, H\X, A)) where H denotes the Tate cohomology ofir [l, Chapter 12 ] and H'(X, A) is the jth Cech cohomology group of (X, A) with arbitrary coefficients and with w action induced by…

### Classification of the actions of the circle on 3-manifolds

- Mathematics
- 1968

(The manifold M6,g,h,t is an explicit sum of handles and p2 X S1's. The L'(Pt, v1)'s are lens spaces each with a specific, or "standard," action. This is described more precisely in the text.) Since…

### Topological Transformation Groups

- Mathematics
- 1956

1. Introduction This note will summarize some of the recent work on topological groups and discuss a few topics in transformation groups mainly in S 3 and S 4. In one aspect of this subject, namely…

### Algebraic Topology

- Mathematics

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.