JOURNAL BROWSE
Search
Advanced SearchSearch Tips
MULTICOMPLEXES, BOUNDED COHOMOLOGY AND ADDITIVITY OF SIMPLICIAL VOLUME
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
MULTICOMPLEXES, BOUNDED COHOMOLOGY AND ADDITIVITY OF SIMPLICIAL VOLUME
KUESSNER, THILO;
  PDF(new window)
 Abstract
We discuss some additivity properties of the simplicial volume for manifolds with boundary: we give proofs of additivity for glueing amenable boundary components and of superadditivity for glueing amenable submanifolds of the boundary, and we discuss doubling of 3-manifolds.
 Keywords
simplicial volume;
 Language
English
 Cited by
1.
A quantitative version of a theorem by Jungreis, Geometriae Dedicata, 2017, 187, 1, 199  crossref(new windwow)
 References
1.
M. Bucher, M. Burger, R. Frigerio, A. Iozzi, C. Pagliantini, and M. B. Pozzetti, Isometric embeddings in bounded cohomology, J. Topol. Anal. 6 (2014), no. 1, 1-25. crossref(new window)

2.
M. Bucher, R. Frigerio, and C. Pagliantini, The simplicial volume of 3-manifolds with boundary, J. Topol. 8 (2015), no. 2, 457-475. crossref(new window)

3.
M. Gromov, Volume and bounded cohomology, Publ. Math. Inst. Hautes Etudes Sci. (1982), no. 56, 5-99

4.
N. Ivanov, Foundations of the theory of bounded cohomology, J. Sov. Math. 37 (1987), 1090-1114. crossref(new window)

5.
D. Jungreis, Chains that realize the Gromov invariant of hyperbolic manifolds, Ergodic Theory Dynam. Systems 17 (1997), no. 3, 643-648. crossref(new window)

6.
S. Kim and T. Kuessner, Simplicial volume of compact manifolds with amenable boundary, J. Topol. Anal. 7 (2015), no. 1, 23-46. crossref(new window)

7.
T. Kuessner, Gromov Volume of Compact Manifolds, Diplomarbeit, FU Berlin, 1996.

8.
T. Kuessner, Efficient fundamental cycles of cusped hyperbolic manifolds, Pacific J. Math. 211 (2003), no. 2 283-314. crossref(new window)

9.
T. Kuessner, Generalizations of Agol's inequality and nonexistence of tight laminations, Pacific J. Math. 251 (2011), no. 1, 109-172. crossref(new window)

10.
S. Matsumoto and S. Morita, Bounded cohomology of certain groups of homeomorphisms, Proc. Amer. Math. Soc. 94 (1985), no. 3, 539-544. crossref(new window)

11.
J. P. May, Simplicial objects in algebraic topology, Chicago Lect. Math., UCP, 1992.

12.
W. Neumann and G. Swarup, Canonical decompositions of 3-manifolds, Geom. Topol. 1 (1997), 21-40. crossref(new window)

13.
H. Park, Relative bounded cohomology, Topology Appl. 131 (2003), no. 3, 203-234. crossref(new window)

14.
T. Soma, The Gromov invariant of links, Invent. Math. 64 (1981), no. 3, 445-454. crossref(new window)

15.
W. Thurston, The geometry and topology of 3-manifolds, Lecture Notes; http://msri.org /publications/books/gt3m.