Morphisms Between Grassmannian Complex and Higher Order Tangent Complex

Sadaqat Hussain, Raziuddin Siddiqui


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.


Tangent Complex; Grassmannian Complex; Cross-ratio; Configuration

Full Text:



J.-L. Cathelineau, Projective configurations, homology of orthogonal groups, and milnor K-theory, Duke Math. J. 121(2) (2004), 343 – 387,

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,

P. Elbaz-Vincent, H. Gangl and M. Kontsevich, On poly(ana)logs I, Compos. Math. 130 (2002), 161 – 210,

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,

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,

S. Hussain and R. Siddiqui, Grassmannian complex and second order tangent complex, Punjab University Journal of Mathematics 48(2) (2016), 1353 – 1363,

R. Siddiqui, Configuration complexes and a variant of Cathelineau’s complex in weight 3, arXiv:1205.3864 [math.NT] (2012),

R. Siddiqui, Configuration Complexes and Tangential and Infinitesimal versions of Polylogarithmic Complexes, Doctoral thesis, Durham University (2010),

R. Siddiqui, Tangent to Bloch-Suslin and Grassmannian complexes over the dual numbers, arXiv:1205.4101v2 [math.NT] (2012),

A. Suslin, Homology of GLn, characteristic classes and Milnor K-theory, Lecture Notes in Mathematics 1046 (1984), 357 – 375,



  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905