Related papers: Inner Cohomology of the General Linear Group
There is an error in the proof of Proposition 3.7. Proposition 3.7 is needed for the proof of the main theorem.
We point out two errors in the paper ``The integer cohomology algebra of toric arrangements'', Adv. Math., Vol. 313, pp. 746-802, 2017. The main error concerns Theorem 4.2.17. In that theorem's proof, Diagram (8) does not commute in general…
There is a serious mistake in the proof.
In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.
A serious error has been found in the paper, specifically, Lemma 8 is incorrect.
We prove a homotopy invariance result for the first cohomology group of the special unitary group $\mathrm{SU}_3(F[t])$ with coefficients in irreducible representations of $\mathrm{PGL}_2(F)$. The main theorem establishes that this…
This paper has been withdrawn due to a crucial error in the proof of the main theorem
A false application of Proposition 4.10 causes a mistake in the proof of Corollary 4.11
This paper has been withdrawn by the author due to a crucial error in formula 4.12.r
Given a complex projective algebraic variety, write H(X) for its cohomology with complex coefficients and IH(X) for its Intersection cohomology. We first show that, under some fairly general conditions, the canonical map H(X)\to IH(X) is…
We point out a mistake in the main statement of \cite{liu} and suggest and proof a correct statement.
This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.
We establish a theorem computing the cohomology groups of line bundles on homogeneous ind-varieties $G/B$ for diagonal ind-groups $G$. The main difficulty in proving this analog of the classical Bott-Borel-Weil theorem is in defining an…
For each prime p, we exhibit pairs of p-groups all of whose integral cohomology groups are isomorphic. The method used involves very little calculation. The groups are exhibited as kernels of homomorphisms from a compact Lie group G to…
This paper have serious error in the proof of main theorem 1.1.Result is not proved.
A very short note, explaining the error in the original paper, which renders its central result incorrect.
The third homology group of GL_n(R) is studied, where R is a `ring with many units' with center Z(R). The main theorem states that if K_1(Z(R))_Q \simeq K_1(R)_Q, (e.g. R a commutative ring or a central simple algebra), then H_3(GL_2(R), Q)…
We introduce the notion of an `inverse property' (IP) quandle C which we propose as the right notion of `Lie algebra' in the category of sets. To any IP quandle we construct an associated group G_C. For a class of IP quandles which we call…
Paper withdrawn - lemma 4.1 was false. Quite a lot of changes need to be made!
This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.