scholarly journals WHAT IS...a Scissors Congruence?

2012 ◽  
Vol 59 (09) ◽  
pp. 1
Author(s):  
Johan L. Dupont
Keyword(s):  
Scissors Congruence

scholarly journals The strong Suslin reciprocity law

2021 ◽  
Vol 157 (4) ◽  
pp. 649-676
Author(s):  
Daniil Rudenko
Keyword(s):  
Rational Functions ◽  
Projective Curve ◽  
Main Ingredient ◽  
Homotopy Invariance ◽  
Reciprocity Law ◽  
Hyperbolic Volume ◽  
Scissors Congruence ◽  
Dehn Invariant ◽  
Contracting Homotopy ◽  
Invariance Theorem

We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The Suslin reciprocity law is a generalization of the Weil reciprocity law to higher Milnor $K$ -theory. The Milnor $K$ -groups can be identified with the top cohomology groups of the polylogarithmic motivic complexes; Goncharov's conjecture predicts the existence of a contracting homotopy underlying Suslin reciprocity. The main ingredient of the proof is a homotopy invariance theorem for the cohomology of the polylogarithmic motivic complexes in the ‘next to Milnor’ degree. We apply these results to the theory of scissors congruences of hyperbolic polytopes. For every triple of rational functions on a compact projective curve over $\mathbb {C}$ we construct a hyperbolic polytope (defined up to scissors congruence). The hyperbolic volume and the Dehn invariant of this polytope can be computed directly from the triple of rational functions on the curve.

scholarly journals Cubic Graphs, Their Ehrhart Quasi-Polynomials, and a Scissors Congruence Phenomenon

2020 ◽  
Vol 65 (1) ◽  
pp. 227-243 ◽  
Author(s):  
Cristina G. Fernandes ◽  
José C. de Pina ◽  
Jorge Luis Ramírez Alfonsín ◽  
Sinai Robins
Keyword(s):  
Cubic Graphs ◽  
Scissors Congruence

scholarly journals Translation Scissors Congruence

1993 ◽  
Vol 100 (1) ◽  
pp. 1-27 ◽  
Author(s):  
R. Morelli
Keyword(s):  
Scissors Congruence
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