Geodesic
The minimum b2 problem for right-angled Artin groups
Hildum, Alyson1
1Deptartment of Mathematics & Statistics, McMaster University, 1280 Main Street West, Hamilton ON L8S 4K1, Canada
Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1599-1641
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This paper focuses on tools for constructing 4–manifolds which have fundamental group G isomorphic to a right-angled Artin group, and which are also minimal in the sense that they minimize b2(M) = dimH2(M; ℚ). For a finitely presented group G, define

In this paper, we explore the ways in which we can bound h(G) from below using group cohomology and the tools necessary to build 4–manifolds that realize these lower bounds. We give solutions for right-angled Artin groups, or RAAGs, when the graph associated to G has no 4–cliques, and further we reduce this problem to the case when the graph is connected and contains only 4–cliques. We then give solutions for many infinite families of RAAGs and provide a conjecture to the solution for all RAAGs.

DOI : 10.2140/agt.2015.15.1599
Classification : 57M05, 20F36
Keywords: Hausmann–Weinberger invariant, right-angled Artin group, RAAG

Hildum, Alyson  1

1 Deptartment of Mathematics & Statistics, McMaster University, 1280 Main Street West, Hamilton ON L8S 4K1, Canada 
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Hildum, Alyson. The minimum b2 problem for right-angled Artin groups. Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1599-1641. doi: 10.2140/agt.2015.15.1599

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