scholarly journals On the Dehn functions of Kähler groups

2020 ◽  
Vol 14 (2) ◽  
pp. 469-488
Author(s):  
Claudio Llosa Isenrich ◽  
Romain Tessera
Keyword(s):  
Dehn Functions ◽  
Kähler Groups

scholarly journals Kähler groups and subdirect products of surface groups

2020 ◽  
Vol 24 (2) ◽  
pp. 971-1017
Author(s):  
Claudio Llosa Isenrich
Keyword(s):  
Surface Groups ◽  
Kähler Groups ◽  
Subdirect Products

scholarly journals ON THE GROWTH OF GROUPS AND AUTOMORPHISMS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 869-874 ◽  
Author(s):  
MARTIN R. BRIDSON
Keyword(s):  
Finitely Generated ◽  
Free Products ◽  
Dehn Functions ◽  
Amalgamated Free Products ◽  
Growth Functions ◽  
Growth Of Groups

We consider the growth functions βΓ(n) of amalgamated free products Γ = A *C B, where A ≅ B are finitely generated, C is free abelian and |A/C| = |A/B| = 2. For every d ∈ ℕ there exist examples with βΓ(n) ≃ nd+1βA(n). There also exist examples with βΓ(n) ≃ en. Similar behavior is exhibited among Dehn functions.

scholarly journals Which 3-manifold groups are Kähler groups?

2009 ◽  
pp. 521-528 ◽  
Author(s):  
Alexandru Dimca ◽  
Alexander Suciu
Keyword(s):  
Kähler Groups

Fibering Kähler manifolds and Kähler groups

1996 ◽  
pp. 21-28
Author(s):  
J. Amorós ◽  
M. Burger ◽  
K. Corlette ◽  
D. Kotschick ◽  
D. Toledo
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kähler Groups

Mini-Workshop: Kähler Groups

2014 ◽  
Vol 11 (1) ◽  
pp. 531-553
Author(s):  
Dieter Kotschick ◽  
Domingo Toledo
Keyword(s):  
Kähler Groups

scholarly journals Taming the hydra: The word problem and extreme integer compression

2018 ◽  
Vol 28 (07) ◽  
pp. 1299-1381
Author(s):  
W. Dison ◽  
E. Einstein ◽  
T. R. Riley
Keyword(s):  
Word Problem ◽  
Polynomial Time ◽  
Complexity Measure ◽  
Dehn Function ◽  
Dehn Functions ◽  
Fast Growing ◽  
Defining Relations ◽  
Finitely Presented Group ◽  
Direct Attack ◽  
Finitely Presented

For a finitely presented group, the word problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is a complexity measure of a direct attack on the word problem by applying the defining relations. Dison and Riley showed that a “hydra phenomenon” gives rise to novel groups with extremely fast growing (Ackermannian) Dehn functions. Here, we show that nevertheless, there are efficient (polynomial time) solutions to the word problems of these groups. Our main innovation is a means of computing efficiently with enormous integers which are represented in compressed forms by strings of Ackermann functions.

Second Order Dehn Functions of Groups

1998 ◽  
Vol 49 (1) ◽  
pp. 1-30 ◽  
Author(s):  
J. M. Alonso ◽  
W. A. Bogley ◽  
R. M. Burton ◽  
S. J. Pride ◽  
X. Wang
Keyword(s):  
Second Order ◽  
Dehn Functions
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