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I would be interested in recommendations for easily accessible/somehow simply readable texts to Cochran-Orr-Teichner's filtrations on knot concordance:

Tim D. Cochran, Kent E. Orr, and Peter Teichner. "Knot concordance, Whitney towers and L2-signatures." Annals of Mathematics (2003): 433-519.

Any suggestions will be appreciated.

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There are summarys of parts of Cochran, Teichner and Orr's paper in:

You'll find all of these references (and I'm sure more besides) at Andrew Ranicki's webpage.

Disclaimer: I'm not a geometric topologist, but as I was in Edinburgh around the time I ended up as one of the examiners of Julia Collins' thesis.

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  1. This is the monograph of J. C. Cha which discusses the rational version of filtrations of knot concordance groups comparing with the original paper.

Cha, Jae Choon. The structure of the rational concordance group of knots. Vol. 182. American Mathematical Soc., 2007.

  1. The following article includes a very nice application of Cochran-Orr-Teichner's work. Here, J. Collins reproved the classical theorem of Casson and Gordon about the sliceness of twist knots.

Collins, Julia. "The $L^2$ signature of torus knots." arXiv preprint arXiv:1001.1329 (2010).

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