Degree three cohomological invariants of semisimple groups

Alexander Merkurjev

Displaying similar documents to “Degree three cohomological invariants of semisimple groups”

Asymptotic Vassiliev invariants for vector fields

Sebastian Baader, Julien Marché (2012)

Bulletin de la Société Mathématique de France

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We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of $ℝ^{3}$ . More precisely, we show that the asymptotics of Vassiliev invariants is completely determined by the helicity of the vector field.

Welschinger invariants of small non-toric Del Pezzo surfaces

Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin (2013)

Journal of the European Mathematical Society

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We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at $\sim q$ real and $s \leq 1$ pairs of conjugate imaginary points, where $q + 2 s \leq 5$ , and the real quadric blown up at $s \leq 1$ pairs of conjugate imaginary points and having non-empty real part. The formula is similar to Vakil’s recursive formula [22] for Gromov–Witten invariants of these surfaces and generalizes our recursive formula [12] for purely real Welschinger invariants...

Smooth invariants and $ω$ -graded modules over $k [X]$

Fred Richman (2000)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that every $ω$ -graded module over $k [X]$ is a direct sum of cyclics. The invariants for such modules are exactly the smooth invariants of valuated abelian $p$ -groups.

Two cases when $d_{κ}$ and $d *_{κ}$ are equal

Ofer Shafir (2001)

Fundamenta Mathematicae

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We deal with two cardinal invariants and give conditions on their equality using Shelah's pcf theory.

Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi (2014)

Annales de l’institut Fourier

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In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type $☆$ ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type $☆$ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...

Generalised Weber functions

Andreas Enge, François Morain (2014)

Acta Arithmetica

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A generalised Weber function is given by $_{N} (z) = η (z / N) / η (z)$ , where η(z) is the Dedekind function and N is any integer; the original function corresponds to N=2. We classify the cases where some power $_{N}^{e}$ evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating $_{N} (z)$ and j(z). Our ultimate goal is the use of these invariants in...

Analytic invariants for the $1 : - 1$ resonance

José Pedro Gaivão (2013)

Annales de l’institut Fourier

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Associated to analytic Hamiltonian vector fields in $ℂ^{4}$ having an equilibrium point satisfying a non semisimple $1 : - 1$ resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.

Asymptotic Expansions of Witten-Reshetikhin-Turaev Invariants for Some Simple $3$ -Manifolds

R. J. Lawrence (1995)

Recherche Coopérative sur Programme n°25

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Witten's Conjecture for many four-manifolds of simple type

Paul M. N. Feehan, Thomas G. Leness (2015)

Journal of the European Mathematical Society

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We prove that Witten’s Conjecture [40] on the relationship between the Donaldson and Seiberg-Witten series for a four-manifold of Seiberg-Witten simple type with $b_{1} = 0$ and odd $b_{2}^{+} \geq 3$ follows from our $(3)$ -monopole cobordism formula [6] when the four-manifold has $c_{1}^{2} \geq χ_{h} - 3$ or is abundant.

Plane and layer $(p 2, 2^{l})$ symmetry groups

S. V. Jablan (1990)

Matematički Vesnik

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Invariants of finite groups generated by generalized transvections in the modular case

Xiang Han, Jizhu Nan, Chander K. Gupta (2017)

Czechoslovak Mathematical Journal

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We investigate the invariant rings of two classes of finite groups $G \leq GL (n, F_{q})$ which are generated by a number of generalized transvections with an invariant subspace $H$ over a finite field $F_{q}$ in the modular case. We name these groups generalized transvection groups. One class is concerned with a given invariant subspace which involves roots of unity. Constructing quotient groups and tensors, we deduce the invariant rings and study their Cohen-Macaulay and Gorenstein properties. The other is concerned...

Brunnian local moves of knots and Vassiliev invariants

Akira Yasuhara (2006)

Fundamenta Mathematicae

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K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of $C_{k}$ -moves. In this paper we give another geometric condition in terms of Brunnian local moves. The proof is simple and self-contained.

Plane and layer $(p^{p r i m e}, 2^{l})$ symmetry groups

S. V. Jablan (1990)

Matematički Vesnik

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A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Robert Guralnick, Pham Tiep (2012)

Journal of the European Mathematical Society

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The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age $\leq 1$ . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation....

Groups of simple and multiple antisymmetry of similitude in $E^{2}$

S. V. Jablan (1986)

Matematički Vesnik

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