Twisting cochains and higher torsion

Details Twisting cochains and higher torsion Twisting cochains and higher torsion

2002-12-31

arxiv.org/abs/math/0212383v3

Mathematics

Algebraic Topology

23 pages, 1 figure, dedicated to Edgar Brown. Revised following suggestions by referee

Scientific paper

This paper gives a short summary of the central role played by Ed Brown's "twisting cochains" in higher Franz-Reidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a twisting cochain which is unique up to fiberwise homotopy equivalence. However, when they are based, the difference between two of them is a higher algebraic K-theory class measured by higher FR torsion. Flat superconnections are also equivalent to twisting cochains.

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