Morphisms Between Grassmannian Complex and Higher Order Tangent Complex
DOI:
https://doi.org/10.26713/cma.v10i3.1220Keywords:
Tangent Complex, Grassmannian Complex, Cross-ratio, ConfigurationAbstract
In this article we extend the notion of tangent complex to higher order and propose morphisms between Grassmannian subcomplex and the tangent dialogarithmic complex for a general order. Moreover, we connect both these complexes and prove the commutativity of resulting diagram. The interesting point is the reappearance of classical Newton's Identities here in a completely different context to the one he had.
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J.-L. Cathelineau, Projective configurations, homology of orthogonal groups, and milnor K-theory, Duke Math. J. 121(2) (2004), 343 – 387, https://projecteuclid.org/euclid.dmj/1076621988.
J.-L. Cathelineau, The tangent complex to the Bloch-Suslin complex, Bull. Soc. Math. France 135 (2007), 565 – 597, DOI: 10.24033/bsmf.2546.
B. H. Dayton, Theory of Equations, Lesson No. 10, Northeastern Illinois University Chicago, IL 60625, USA, http://barryhdayton.space/theoryEquations/textpartX.pdf.
P. Elbaz-Vincent, H. Gangl and M. Kontsevich, On poly(ana)logs I, Compos. Math. 130 (2002), 161 – 210, https://arxiv.org/abs/math/0008089.
A. B. Goncharov, Euclidean Scissors congruence groups and mixed Tate motives over dual numbers, Math. Res. Lett. 11 (2004), 771 – 784, DOI: 10.4310/MRL.2004.v11.n6.95.
A. B. Goncharov, Explicit construction of characteristic classes, Advances in Soviet Mathematics, I. M. Gelfand Seminar 1, 16 (1993), 169 – 210, https://gauss.math.yale.edu/~ag727/4821.
A. B. Goncharov, Geometry of configurations, polylogarithms and Motivic cohomology, Adv. Math. 114(2) (1995), 197 – 318, DOI: 10.1006/aima.1995.1045.
A. B. Goncharov, Polylogarithms and Motivic Galois groups, in Proceedings of the Seattle Conf. on Motives, July 1991, Seattle, AMS P. Symp. Pure Math. 2, 55 (1994), 43 – 96, https://gauss.math.yale.edu/~ag727/polylog.pdf.
S. Hussain and R. Siddiqui, Grassmannian complex and second order tangent complex, Punjab University Journal of Mathematics 48(2) (2016), 1353 – 1363, http://pu.edu.pk/images/journal/maths/PDF/Paper-8-48-2-16.pdf.
R. Siddiqui, Configuration complexes and a variant of Cathelineau's complex in weight 3, arXiv:1205.3864 [math.NT] (2012), https://arxiv.org/abs/1205.3864.
R. Siddiqui, Configuration Complexes and Tangential and Infinitesimal versions of Polylogarithmic Complexes, Doctoral thesis, Durham University (2010), http://etheses.dur.ac.uk/586/.
R. Siddiqui, Tangent to Bloch-Suslin and Grassmannian complexes over the dual numbers, arXiv:1205.4101v2 [math.NT] (2012), https://arxiv.org/pdf/1205.4101.pdf.
A. Suslin, Homology of GLn, characteristic classes and Milnor K-theory, Lecture Notes in Mathematics 1046 (1984), 357 – 375, https://www.scholars.northwestern.edu/en/publications/homology-of-gln-characteristic-classes-and-milnor-k-theory.
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