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3-torsion in the Ho...
3-torsion in the Homology of Complexes of Graphs of Bounded Degree
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- Jonsson, Jakob (författare)
- KTH,Matematik (Inst.)
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KTH Matematik (Inst) (creator_code:org_t)
- 2013
- 2013
- Engelska.
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Ingår i: Canadian Journal of Mathematics. - 0008-414X .- 1496-4279. ; 65:4, s. 843-862
- Relaterad länk:
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https://urn.kb.se/re...
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visa fler...
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https://doi.org/10.4...
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Abstract
Ämnesord
Stäng
- For delta >= 1 and n >= 1, consider the simplicial complex of graphs on n vertices in which each vertex has degree at most delta; we identify a given graph with its edge set and admit one loop at each vertex. This complex is of some importance in the theory of semigroup algebras. When delta = 1, we obtain the matching complex, for which it is known that there is 3-torsion in degree d of the homology whenever (n - 4)/3 <= d <= (n - 6)/2. This paper establishes similar bounds for delta >= 2. Specifically, there is 3-torsion in degree d whenever (3 delta - 1)n - 8/6 <= d <= delta(n - 1) - 4/2. The procedure for detecting torsion is to construct an explicit cycle z that is easily seen to have the property that 3z is a boundary. Defining a homomorphism that sends z to a non-boundary element in the chain complex of a certain matching complex, we obtain that z itself is a non-boundary. In particular, the homology class of z has order 3.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- simplicial complex
- simplicial homology
- torsion group
- vertex degree
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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