Skip to main content

Tilings and finite energy retractions of locally symmetric spaces

Publication ,  Journal Article
Saper, L
Published in: Commentarii Mathematici Helvetici
January 1, 1997

Let Γ\X̄ be the Borel-Serre compactification of an arithmetic quotient Γ\X of a symmetric space of noncompact type. We construct natural tilings Γ\X̄ = ∐P Γ\X̄P (depending on a parameter b) which generalize the Arthur-Langlands partition of Γ\X. This is applied to yield a natural piecewise analytic deformation retraction of Γ\X̄ onto a compact submanifold with corners Γ\X0 ⊂ Γ\X. In fact, we prove that Γ\X0 is a realization (under a natural piecewise analytic diffeomorphism) of Γ\X̄ inside the interior Γ\X. For application to the theory of harmonic maps and geometric rigidity, we prove this retraction and diffeomorphism have finite energy except for a few low rank examples. We also use tilings to give an explicit description of a cofinal family of neighborhoods of a face of Γ\X̄, and study the dependance of tilings on the parameter b and the degeneration of tilings.

Duke Scholars

Published In

Commentarii Mathematici Helvetici

DOI

ISSN

0010-2571

Publication Date

January 1, 1997

Volume

72

Issue

2

Start / End Page

167 / 201

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Saper, L. (1997). Tilings and finite energy retractions of locally symmetric spaces. Commentarii Mathematici Helvetici, 72(2), 167–201. https://doi.org/10.1007/pl00000369
Saper, L. “Tilings and finite energy retractions of locally symmetric spaces.” Commentarii Mathematici Helvetici 72, no. 2 (January 1, 1997): 167–201. https://doi.org/10.1007/pl00000369.
Saper L. Tilings and finite energy retractions of locally symmetric spaces. Commentarii Mathematici Helvetici. 1997 Jan 1;72(2):167–201.
Saper, L. “Tilings and finite energy retractions of locally symmetric spaces.” Commentarii Mathematici Helvetici, vol. 72, no. 2, Jan. 1997, pp. 167–201. Scopus, doi:10.1007/pl00000369.
Saper L. Tilings and finite energy retractions of locally symmetric spaces. Commentarii Mathematici Helvetici. 1997 Jan 1;72(2):167–201.

Published In

Commentarii Mathematici Helvetici

DOI

ISSN

0010-2571

Publication Date

January 1, 1997

Volume

72

Issue

2

Start / End Page

167 / 201

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics