Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

FOUNDATIONS OF THE THEORY OF ℓ1 HOMOLOGY

  • Published : 2004.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we provide the algebraic foundations to the theory of relative $\ell$$_1$ homology. In particular, we prove that $\ell$$_1$ homology of topological spaces, both for the absolute case and for the relative case, depends only on their fundamental groups. We also provide a .proof of Gromov's Equivalence theorem for $\ell$$_1$ homology, stated by Gromov without proof [4].

Keywords

References

  1. Ann.of Math. Stud. v.97 Some remarks on bounded cohomology R.Brooks
  2. Cohomology of Groups K.S.Brown
  3. J. London Math. Soc. v.202 Some results on bounded cohomology R.I.Grigorchuk
  4. Publ. Math. IHES v.56 Volume and bounded cohomology M.Gromov
  5. J. Soviet Math. v.37 Foundation of theory of bounded cohomology N.Ivanov https://doi.org/10.1007/BF01086634
  6. Proc. Amer. Math. Soc. v.94 Bounded cohomology of certain groups of homeomorphisms S.Matsumoto;S.Morita https://doi.org/10.2307/2045250
  7. Topology v.23 Bounded cohomology and l₁-homology of surfaces Y.Mitsumatsu https://doi.org/10.1016/0040-9383(84)90006-5
  8. Topology Appl. v.131 Relative bounded cohomology H.Park https://doi.org/10.1016/S0166-8641(02)00339-5

Cited by

  1. Relative measure homology and continuous bounded cohomology of topological pairs vol.257, pp.1, 2012, https://doi.org/10.2140/pjm.2012.257.91
  2. Isometric embeddings in bounded cohomology vol.06, pp.01, 2014, https://doi.org/10.1142/S1793525314500058