Co-rank and Betti number of a group

Title:

Co-rank and Betti number of a group

Creator:

Gelbukh, Irina

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:96092b91-3234-46ce-adda-252a8f97445d
uuid:96092b91-3234-46ce-adda-252a8f97445d
issn:0011-4642

Subject:

mathematics, co-rank, inner rank, fundamental group, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group’s rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is additive with respect to the free product and the direct product of groups. Our results are important for the theory of foliations and for manifold topology, where the corresponding notions are related with the cut-number (or genus) and the isotropy index of the manifold, as well as with the operations of connected sum and direct product of manifolds., Irina Gelbukh., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

565-567

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:2

Harvested from:

CDK

Metadata only:

false