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5 papers · 2 filters
Homotopical Intersection Theory, III: multi-relative intersection problems
John R. Klein, Bruce Williams
This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of…
Kirchhoff's theorems in higher dimensions and Reidemeister torsion
Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein
Using ideas from algebraic topology and statistical mechanics, we generalize Kirchhoff's network and matrix-tree theorems to finite CW complexes of arbitrary dimension. As an appli…
On Kirchhoff's theorems with coefficients in a line bundle
Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein
We prove `twisted' versions of Kirchhoff's network theorem and Kirchhoff's matrix-tree theorem on connected finite graphs. Twisting here refers to chains with coefficients in a fla…
Totalization of simplicial homotopy types
Crichton Ogle, Andrew Salch
We identify the obstructions for the functoriality and the uniqueness of the totalization functor, (partially) defined on the category of simplicial objects in the homotopy categor…
Algebraic topology and the quantization of fluctuating currents
Vladimir Y. Chernyak, John R. Klein, Nikolai A. Sinitsyn
We give a new approach to the study of statistical mechanical systems: algebraic topology is used to investigate the statistical distributions of stochastic currents generated in g…