Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-30T22:33:18.703Z Has data issue: false hasContentIssue false
  • English
  • Français

Nontriviality results for the characteristic algebra of a DGA

Published online by Cambridge University Press:  28 July 2016

GEORGIOS DIMITROGLOU RIZELL
GEORGIOS DIMITROGLOU RIZELL*
Affiliation:
Centre for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0WB. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Assume that we are given a semifree noncommutative differential graded algebra (DGA for short) whose differential respects an action filtration. We show that the canonical unital algebra map from the homology of the DGA to its characteristic algebra, i.e. the quotient of the underlying algebra by the two-sided ideal generated by the boundaries, is a monomorphism. The main tool that we use is the weak division algorithm in free noncommutative algebras due to P. Cohn.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 3 , May 2017 , pp. 419 - 433
Copyright
Copyright © Cambridge Philosophical Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[Che] Chekanov, Y. Differential algebra of Legendrian links. Invent. Math. 150 (3) (2002), 441–483.Google Scholar
[Coh] Cohn, P. M. Free Ideal Rings and Localisation in General Rings (Cambridge University Press, 2006).Google Scholar
[DR] Rizell, G. Dimitroglou Exact Lagrangian caps and non-uniruled Lagrangian submanifolds. Ark. Mat. 53 (1) (2015), 37–64.Google Scholar
[DRG] Rizell, G. Dimitroglou and Golovko, R.. Estimating the number of Reeb chords using a linear representation of the characteristic algebra. Algebr. Geom. Topol. 15 (5) (2015), 2887–2920.CrossRefGoogle Scholar
[EES1] Ekholm, T., Etnyre, J. and Sullivan, M. The contact homology of Legendrian submanifolds in R 2n+1 . J. Differential Geom. 71 (2) (2005), 177–305.CrossRefGoogle Scholar
[EES2] Ekholm, T. and Etnyre, J. and Sullivan, M. Non-isotopic Legendrian submanifolds in R 2n+1 . J. Differential Geom. 71 (2005), 85–128.CrossRefGoogle Scholar
[EES3] Ekholm, T. and Etnyre, J. and Sullivan, M. Legendrian contact homology in P × R . Trans. Amer. Math. Soc. 359 (7) (2007), 3301–3335.Google Scholar
[Eli] Eliashberg, Y. Invariants in contact topology. Doc. Math. Extra Vol. II (1998), 327–338.Google Scholar
[EGH] Eliashberg, Y. and Givental, A. and Hofer, H. Introduction to symplectic field theory. Geom. Funct. Anal. Special Volume, Part II (2000), 560–673.Google Scholar
[Ng] Ng, L. Computable Legendrian invariants. Topology 42 (1) (2003), 55–82.Google Scholar
[Siv] Sivek, S. The contact homology of Legendrian knots with maximal Thurston–Bennequin invariant. J. Symplectic Geom. 11 (2) (2013), 167–178.Google Scholar
[Sul] Sullivan, D. Infinitesimal computations in topology. Inst. Hautes Études Sci. Publ. Math. 47 (1978), 269–331.Google Scholar