Homotopy theory of bicomplexes
Copyright policy )Homotopy theory of bicomplexes
We define two model structures on the category of bicomplexes concentrated in the right half plane. The first model structure has weak equivalences detected by the totalisation functor. The second model structure's weak equivalences are detected by the $E^2$-term of the spectral sequence associated to the filtration of the total complex by the horizontal degree. We then extend this result to twisted complexes.
26 pages
- University of Seville Spain
- University of Kent United Kingdom
model category, Bicomplexes, Abstract and axiomatic homotopy theory in algebraic topology, weak equivalence, K-Theory and Homology (math.KT), Nonabelian homotopical algebra, bicomplexe, totalisation functor, twisted complex, QA150, spectral sequence, Mathematics - K-Theory and Homology, FOS: Mathematics, Algebraic Topology (math.AT), Homotopy, Mathematics - Algebraic Topology, QA
model category, Bicomplexes, Abstract and axiomatic homotopy theory in algebraic topology, weak equivalence, K-Theory and Homology (math.KT), Nonabelian homotopical algebra, bicomplexe, totalisation functor, twisted complex, QA150, spectral sequence, Mathematics - K-Theory and Homology, FOS: Mathematics, Algebraic Topology (math.AT), Homotopy, Mathematics - Algebraic Topology, QA
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