Geodesic
Homotopy and homology of finite lattices
The electronic journal of combinatorics, Tome 10 (2003)
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We exhibit an explicit homotopy equivalence between the geometric realizations of the order complex of a finite lattice and the simplicial complex of coreless sets of atoms whose join is not ${}\hat 1{}$. This result, which extends a theorem of Segev, leads to a description of the homology of a finite lattice, extending a result of Björner for geometric lattices.
DOI : 10.37236/1723
Classification : 06A11, 06C10
Mots-clés : homotopy equivalence, order complex of a finite lattice, simplicial complex of coreless sets of atoms, homology, geometric lattices 
@article{10_37236_1723,
     author = {Andreas Blass},
     title = {Homotopy and homology of finite lattices},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1723},
     zbl = {1025.06002},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1723/}
}
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Andreas Blass. Homotopy and homology of finite lattices. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1723

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