Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Differential Geometry

arXiv:0710.3770 (math)
[Submitted on 19 Oct 2007 (v1), last revised 16 Nov 2007 (this version, v3)]

Title:Cohomogeneity one manifolds and selfmaps of nontrivial degree

Authors:Thomas Puettmann
View PDF
Abstract: We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).
Comments: v2, v3: minor improvements
Subjects: Differential Geometry (math.DG); Algebraic Topology (math.AT)
MSC classes: 57S15, 55M25
Cite as: arXiv:0710.3770 [math.DG]
  (or arXiv:0710.3770v3 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.3770
Journal reference: Transform. Groups 14 (2009), 225-247
Related DOI: https://doi.org/10.1007/s00031-008-9037-6

Submission history

From: Thomas Puettmann [view email]
[v1] Fri, 19 Oct 2007 19:59:54 UTC (13 KB)
[v2] Sun, 28 Oct 2007 01:14:38 UTC (13 KB)
[v3] Fri, 16 Nov 2007 22:16:05 UTC (13 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.DG
< prev   |   next >
new | recent | 2007-10
Change to browse by:
math
math.AT

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)