Last edited by Mir
Monday, July 20, 2020 | History

8 edition of Scissors Congruences, Group Homology and Characteristic Classes (Nankai Tracts in Mathematics, V. 1.) found in the catalog.

# Scissors Congruences, Group Homology and Characteristic Classes (Nankai Tracts in Mathematics, V. 1.)

## by Johan L. Dupont

Written in English

Subjects:
• Euclidean geometry,
• Topology,
• Mathematics,
• Science/Mathematics,
• Geometry - General,
• Characteristic classes,
• Topology - General,
• Tetrahedra,
• Volume (Cubic content)

• The Physical Object
FormatPaperback
Number of Pages168
ID Numbers
Open LibraryOL9195299M
ISBN 109810245084
ISBN 109789810245085

For spherical scissors congruence the $+1$-eigenspace appears. This can be found in papers of Dupont, Sah, or the book "Scissors congruences, group homology and characteristic classes" by . There is a book. J.L. Dupont, Scissors congruences, group homology and characteristic classes .ps), Lecture notes from Nankai Institute of Mathematics, , (which is from ) and its role in understanding the 19th century scissors congruence The subject is very active now.

the s.c. group P(X) is closely related to the homology groups of the isometry group for the geometry of X as a discrete group. In fact, GH3 is related to diﬃcult problems in homological algebra and algebraic the following we shall concentrate on the cases X = S3, re- . We show in this work that homology in degree d of a congruence group, in a very general framework, defines a weakly polynomial functor (in the sense of [Djament-Vespa, "foncteurs faiblement.

S-units and S-class group in algebraic function fields J ALGEBRA; Michael Rosen; View. Scissors congruences, group homology and characteristic classes realization is a closed orientable.   As before G denotes a complex reductive Lie group, g its Lie algebra, and Gthe underlying discrete group. Thus, constructing characteristic classes with coefficients in Vfor flat G-bundles, is equivalent to defining characteristic homomorphisms H*(BGa)--> V () where BGs is the classifying space for G As usual (cf. e.g. [10]) BG= II NG' II.

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### Scissors Congruences, Group Homology and Characteristic Classes (Nankai Tracts in Mathematics, V. 1.) by Johan L. Dupont Download PDF EPUB FB2

Scissors Congruences, Group Homology and Characteristic Classes (Nankai Tracts in Mathematics) by Johan L DuPont (Author), Weiping Zhang (Editor) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The digit Group Homology and Characteristic Classes book 10 Cited by:   The book starts from the classical solution of this problem by M Dehn.

But generalization to higher dimensions and other geometries quickly leads to a great variety of mathematical topics, such as homology of groups, algebraic K-theory, characteristic classes for flat bundles, and invariants for hyperbolic manifolds.

Introduction and History -- Ch. Scissors congruence group and homology -- Ch. Homology of flag complexes -- Ch. Translational scissors congruences -- Ch. Euclidean scissors congruences -- Ch.

Sydler\'s theorem and non-commutative differential forms -- Ch. Spherical scissors congruences -- Ch. Hyperbolic scissors congruence. Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc.

Search. Group Homology and Characteristic Classes, pp. i-viii () No Access. Scissors Congruences, Group Homology and Characteristic Classes. Metrics. Downloaded 37 times. One can look at the recent book of Dupont (Scissors Congruences, Scissors Congruences Homology and Characteristic Classes, Nankai Tracts in Mathematics, Vol.

1, World Scientic, Singapore, ) to get an idea of the richness and state of the problem. At this point it must now be clear that there are needed some homology calculations of the isometry groups for the 3 geometries and related Lie groups considered as discrete groups.

This subject was first considered in connection with the theory of characteristic classes for foliations (see e.g. [ Kamber-Tondeur, ], [ Cheeger-Simons, ]). Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc.

Group Homology and Characteristic Classes, pp. () No Access. Homology of flag complexes. Scissors Congruences, Group Homology and Characteristic Classes.

Metrics. The following article would like to yet reinforce it. One can look at the recent book of Dupont (Scissors Congruences, Group Homology and Characteristic Classes, Nankai Tracts in Mathematics, Vol.

1, World Scientific, Singapore, ) to get. Abstract: For the study of the structure of the scissors congruence groups in spherical and hyperbolic 3-space a basic ingredient was the exact sequence in theorem relating the homology of Sl (2, F), F a field of characteristic 0, with the group generated by cross-ratios of four points on the projective line P 1 (F).

In the remaining chapters we shall outline a similar program for. Johan L Dupont Scissors Congruences, Group Homology And Characteristic Classes; Boltjansky, V.

Hilbert’s Third Problem. John Wiley & Sons Inc. ヒルベルトの第3問題（ヒルベルトのだい3もんだい、英: Hilbert's third problem ）は年に提出された問題で、ヒルベルトの23の問題のうち最も早く解決されたものである。 問題は次の問いと関係している：「同体積の多面体が2個与えられたとき、一方を有限個の多面体に切断して組み換えることで.

I have seen this conjecture attributed to Bloch somewhere, and in Dupont's book "Scissors congruences, group homology and characteristic classes" it is attributed to Sah. What's the exact history. Now for the actual mathematical questions.

On homological stability for orthogonal and special orthogonal groups Nakada, Masayuki, Kyoto Journal of Mathematics, ; Stability for closed surfaces in a background space Cohen, Ralph L. and Madsen, Ib, Homology, Homotopy and Applications, ; Totally twisted Khovanov homology Roberts, Lawrence, Geometry & Topology, ; On subgroups of the additive group in differentially closed.

One can look at the recent book of Dupont (Scissors Congruences, Group Homology and Characteristic Classes, Nankai Tracts in Mathematics, Vol. Scissors Congruences, Group Homology and Characteristic Classes, OpenURL Placeholder Text [11] Dupont.

L., Sah. C.-H. Scissors Congruences. II, Journal of Pure and Applied Algebra Euclidean Scissors Congruence Groups and Mixed Tate Motives Over Dual Numbers. Get this from a library. Scissors congruences, group homology and characteristic classes.

[Johan L Dupont] -- These lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of They provide an overview of.

Scissors congruences, group homology and characteristic classes, Nankai Tracts in Math., 1, World Scientific (). Update: As mentioned below, the answer to the original question is a strong No. However, the case of $\\pi_4$ remains, and actually I think that this one would follow from Suslin's conjecture on.

Two polygons in the Eucledean plane P, P ′ P,P' have the same area iff they are scissors congruent in the sense that they can be subdivided into finitely many pieces such that each piece of P P is congruent In the book. J.L. Dupont, Scissors congruences, group homology and characteristic classes .ps), Lecture notes from Nankai Institute.

The following article would like to yet reinforce it. One can look at the recent book of Dupont (Scissors Congruences, Group Homology and Characteristic Classes, Nankai Tracts in Mathematics, Vol.

1, World Scientific, Singapore, ) to get an idea of the richness and state of the problem. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share .Scissors Congruences, Group Homology And Characteristic Classes (ISBN ) bestellen.

Schnelle Lieferung, auch auf Rechnung - Relationship between scissors congruence in 3d hyperbolic and spherical geometry, and the homology of SL(2,C) made discrete.- Definition of the Cheeger-Chern-Simons (CCS) class and proof that volume and Dehn invariant are sufficient to detect scissors congruence in 3d hyperbolic and spherical geometry if and only if the CCS class is injective.