Blocked-braid Groups
D. Maglia, N. Sabadini, R.F.C. Walters

TL;DR
The paper introduces blocked-braid groups, a new family of groups derived from braid groups with geometric modifications, exploring their algebraic properties and connections to Frobenius algebras.
Contribution
It defines the blocked-braid groups, analyzes their structure, and establishes their finiteness for small n and infiniteness for larger n.
Findings
Blocked-braid groups are finite for n=1,2,3.
Blocked-braid groups are infinite for n>3.
Dirac's Belt Trick holds in these groups.
Abstract
We introduce and study a family of groups , called the blocked-braid groups, which are quotients of Artin's braid groups , and have the corresponding symmetric groups as quotients. They are defined by adding a certain class of geometrical modifications to braids. They arise in the study of commutative Frobenius algebras and tangle algebras in braided strict monoidal categories. A fundamental equation true in is Dirac's Belt Trick; that torsion through is equal to the identity. We show that is finite for and 3 but infinite for .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology
