Skip to main content
SpringerLink
Log in

Mutants of compactified representations revisited

  • Original Article
  • Published:
Boletín de la Sociedad Matemática Mexicana Aims and scope Submit manuscript

Abstract

We show that the mutants of compactified representations constructed by Franz and Puppe can be written as intersections of real quadrics involving division algebras and as generalizations of polygon spaces. We also show that these manifolds are connected sums of products of spheres.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Allday, C., Franz, M., Puppe, V.: Equivariant cohomology, syzygies and orbit structure. Trans. Am. Math. Soc. 366, 6567–6589 (2014). doi:10.1090/S0002-9947-2014-06165-5

    Article  MathSciNet  MATH  Google Scholar 

  2. Allday, C., Puppe, V.: Cohomological Methods in Transformation Groups. Cambridge University Press, Cambridge (1993). doi:10.1017/CBO9780511526275

  3. Baez, J.C.: The octonions. Bull. Am. Math. Soc. 39, 145–205 (2002). doi:10.1090/S0273-0979-01-00934-X

    Article  MathSciNet  MATH  Google Scholar 

  4. Conway, J.H., Smith, D.A.: On Quaternions and Octonions. A K Peters, Natick (2003)

    MATH  Google Scholar 

  5. Ebbinghaus, H.-D., et al.: Numbers. Springer, New York (1991). doi:10.1007/978-1-4612-1005-4

  6. Franz, M.: Big polygon spaces. Int. Math. Res. Not. 2015, 13379–13405 (2015). doi:10.1093/imrn/rnv090

    Article  MathSciNet  MATH  Google Scholar 

  7. Franz, M.: A quotient criterion for syzygies in equivariant cohomology. Transform. Groups (to appear). arXiv:1205.4462v3

  8. Franz, M., Puppe, V.: Freeness of equivariant cohomology and mutants of compactified representations, pp. 87–98. In: Harada, M., et al. (eds.) Toric Topology (Osaka, 2006). Contemporary Mathematics, vol. 460. AMS, Providence (2008). doi:10.1090/conm/460/09012

  9. Gitler, S.: López de Medrano, S.: Intersections of quadrics, moment-angle manifolds and connected sums. Geom. Topol. 17, 1497–1534 (2013). doi:10.2140/gt.2013.17.1497

    Article  MathSciNet  MATH  Google Scholar 

  10. Goertsches, O., Rollenske, S.: Torsion in equivariant cohomology and Cohen-Macaulay \(G\)-actions. Transform. Groups 16, 1063–1080 (2011). doi:10.1007/s00031-011-9154-5

    Article  MathSciNet  MATH  Google Scholar 

  11. Gómez Gutiérrez, V., López de Medrano, S.: Topology of the intersections of quadrics II. Bol. Soc. Mat. Mex. 20, 237–255 (2014). doi:10.1007/s40590-014-0038-2

  12. Kosinski, A.A.: Differential Manifolds. Academic Press, Boston (1993)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada

    Matthias Franz

  2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, 04510, México, Mexico

    Santiago López de Medrano

  3. Department of Mathematics, University of Toronto, Toronto, ON, M5S 1A2, Canada

    John Malik

Authors
  1. Matthias Franz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Santiago López de Medrano
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John Malik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matthias Franz.

Additional information

To the memory of Sam Gitler.

M. F. was supported by an NSERC Discovery Grant and J. M. by an NSERC USRA.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Franz, M., López de Medrano, S. & Malik, J. Mutants of compactified representations revisited. Bol. Soc. Mat. Mex. 23, 511–526 (2017). https://doi.org/10.1007/s40590-016-0128-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40590-016-0128-4

Mathematics Subject Classification

Search

Navigation