Graph braid groups and right-angled Artin groups

Kim, Jee Hyoun; Ko, Ki Hyoung; Park, Jungchan

doi:10.48550/arxiv.0805.0082

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This Allows Us To Define a Boundary Morphism1

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2018

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“…Kim, Ko, and Park proved that G is planar if and only if H 1 (B 2 G, Z) is torsion free in [KKP,Theorem 5.5]. It is also conjectured in that work that Theorem 2.17 is true.…”

Section: This Allows Us To Define a Boundary Morphismmentioning

confidence: 93%

Stability phenomena in the homology of tree braid groups

Ramos

2018

Algebr. Geom. Topol.

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For a tree G, we study the changing behaviors in the homology groups H i (B n G) as n varies, where B n G := π 1 (UConf n (G)). We prove that the ranks of these homologies can be described by a single polynomial for all n, and construct this polynomial explicitly in terms of invariants of the tree G. To accomplish this we prove that the group n H i (B n G) can be endowed with the structure of a finitely generated graded module over an integral polynomial ring, and further prove that it naturally decomposes as a direct sum of graded shifts of squarefree monomial ideals. Following this, we spend time considering how our methods might be generalized to braid groups of arbitrary graphs, and make various conjectures in this direction.

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“…Kim, Ko, and Park proved that G is planar if and only if H 1 (B 2 G, Z) is torsion free in [KKP,Theorem 5.5]. It is also conjectured in that work that Theorem 2.17 is true.…”

Section: This Allows Us To Define a Boundary Morphismmentioning

confidence: 93%

Stability phenomena in the homology of tree braid groups

Ramos

2018

Algebr. Geom. Topol.

View full text Add to dashboard Cite

show abstract

Graph braid groups and right-angled Artin groups

Cited by 1 publication

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Stability phenomena in the homology of tree braid groups

Stability phenomena in the homology of tree braid groups

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