On the Fixed Point Formula

Lefschetz, Solomon

doi:10.2307/1968838

Cited by 48 publications

(45 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…I will prove them using the character theory of G, the Lefshetz fixed point formula [21] (which dates from approximately the same period as Hecke's work), and a holomorphic refinement of this fixed point formula. The general line argument is similar to that in Hecke's original papers.…”

Section: Introductionmentioning

confidence: 94%

On Hecke’s decomposition of the regular differentials on the modular curve of prime level

Gross

2018

Res Math Sci

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 94%

On Hecke’s decomposition of the regular differentials on the modular curve of prime level

Gross

2018

Res Math Sci

View full text Add to dashboard Cite

show abstract

“…Using the functoriality of Remark 4.11, the second assertion of the Corollary now follows from the first assertion and Lemma 4.12. ✷ Scheme: Our strategy to extend the techniques of Theorem 4.3 (b) beyond spheres to Poincaré duality PD(2n+1) groups (to ensure even dimensional boundary) is as follows: 1) Recall a consequence of an old Theorem of Lefschetz [Lef34], [Lef37] 2) Use Theorem 2.11 (or Corollary 4.13 Assertion 1) due to Bestvina that the boundary of a hyperbolic PD(m) group over the integers is a homological manifold (in fact a homology sphere) with locally connected boundary. 3) Finally use Corollary 4.13 Assertion 2 to conclude that the homeomorphisms of the homological manifolds we have, moving points through very small distances, induce the identity map on homology.…”

Section: Manifolds and Codimension One Duality Subgroupsmentioning

confidence: 99%

Pattern rigidity in hyperbolic spaces: duality and PD subgroups

Biswas¹,

Mj²

2012

Groups Geom. Dyn.

View full text Add to dashboard Cite

Abstract. For i = 1, 2, let G i be cocompact groups of isometries of hyperbolic space H n of real dimension n, n ≥ 3. Let H i ⊂ G i be infinite index quasiconvex subgroups satisfying one of the following conditions: 1) limit set of H i is a codimension one topological sphere. 2) limit set of H i is an even dimensional topological sphere.3) H i is a codimension one duality group. This generalizes (1). In particular, if n = 3, H i could be any freely indecomposable subgroup of G i . 4) H i is an odd-dimensional Poincaré Duality group P D(2k + 1). This generalizes (2). We prove pattern rigidity for such pairs extending work of Schwartz who proved pattern rigidity when H i is cyclic. All this generalizes to quasiconvex subgroups of uniform lattices in rank one symmetric spaces satisfying one of the conditions (1)- (4), as well as certain special subgroups with disconnected limit sets. In particular, pattern rigidity holds for all quasiconvex subgroups of hyperbolic 3-manifolds that are not virtually free. Combining this with the main result of Mosher-Sageev-Whyte [MSW04], we get quasi-isometric rigidity results for graphs of groups where the vertex groups are uniform lattices in rank one symmetric spaces and edge groups are of any of the above types.This paper is dedicated to the memory of Kalyan Mukherjea.

show abstract

“…De cette manière, la théorie des points fixes de S. LEFSCHETZ [^], [5] sera généralisée dans deux directions :…”

Section: Théorie Des Points Fixes : Sur Les Rétractes De Voisinage Deunclassified

Théorie des points fixes : sur les rétractes de voisinage des espaces convexoïdes

Deleanu¹

1959

Bul. Soc. Math. France

View full text Add to dashboard Cite

On the Fixed Point Formula

Cited by 48 publications

References 0 publications

On Hecke’s decomposition of the regular differentials on the modular curve of prime level

On Hecke’s decomposition of the regular differentials on the modular curve of prime level

Pattern rigidity in hyperbolic spaces: duality and PD subgroups

Théorie des points fixes : sur les rétractes de voisinage des espaces convexoïdes

Contact Info

Product

Resources

About