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Homology of infinite loop spaces
P. 111–121.
We prove a simple homological expression for the homology of a connected spectrum represented by an infinite loop space via the Segal machine. The expression is essentially due to Pirashvili but not stated explicitly in his work; we give an independent proof.
In book
Zürich: European Mathematical Society Publishing house, 2012.
Sokoloff D., Malyshkina R., Margarita V Remizowa et al., Frontiers in Plant Science 2023 Vol. 13 Article 1081981
Understanding the complex inflorescence architecture and developmental morphology of common buckwheat (Fagopyrum esculentum) is crucial for crop yield. However, most published descriptions of early flower and inflorescence development in Polygonaceae are based on light microscopy and often documented by line drawings. In Fagopyrum and many other Polygonaceae, an important inflorescence module is the thyrse, in which the ...
Added: February 20, 2024
Lopatkin V., Сибирский журнал индустриальной математики 2008 Т. 11 № 1 С. 141–151
Изучается одна из математических моделей параллельных вычислительных процессов – асинхронная система переходов. Предложены способы вычисления групп гомологий и многочлена Пуанкаре конечной асинхронной системы переходов. Получены условия разложимости асинхронной системы переходов в параллельное произведение. ...
Added: October 29, 2021
Lopatkin V., Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика 2010 Т. 10 № 2 С. 3–10
The aim of this paper is to define the structure of the ring over the graded cohomology group of a semicubical set with coefficients in a ring with unit. ...
Added: October 29, 2021
Pavutnitskiy F., Ivanov S., Zaikovskii A. et al., Journal of Algebra 2021 Vol. 586 P. 99–139
We study five different types of the homology of a Lie algebra over a commutative ring which are naturally isomorphic over fields. We show that they are not isomorphic over commutative rings, even over , and study connections between them. In particular, we show that they are naturally isomorphic in the case of a Lie ...
Added: October 7, 2021
Kochetkov Y., Фундаментальная и прикладная математика 2014 Т. 19 № 1 С. 45–63
Мы рассматриваем открытое пространство модулей $\mathcal{M}_{2,1}$ комплексных кривых рода 2 с одной отмеченной точкой. На языке хордовых диаграмм мы описываем клеточную структуру пространства $\mathcal{M}_{2,1}$ и структуру примыкания клеток. Это позволяет нам построить матрицы граничных операторов и найти числа Бетти пространства $\mathcal{M}_{2,1}$ над Q. ...
Added: November 11, 2014
Khoroshkin A., Dotsenko V., Algebra & Number Theory 2013 Vol. 7 No. 3 P. 673–700
This paper has been started as a particular application of the method of resolutions via Grobner bases we suggested here. We introduce a notion of a shuffle algebra. A shuffle algebra is a Z+-graded vector space V=∪∞i=1 such that for any pair (i,j) there exists a collection of operations ∗σ:Vi⊗Vj→Vi+j numbered by (i,j)-shuffle permutations σ∈Si+j ...
Added: September 29, 2013
Galkin S., Shinder E., / Series math "arxiv.org". 2012. No. 1210.3339.
We construct quasi-phantom admissible subcategories in the derived category of coherent sheaves on the Beauville surface S. These quasi-phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal possible length 4 on S. We prove that there are exactly 6 exceptional collections consisting of line bundles (up to a twist) and these collections ...
Added: September 14, 2013
Galkin S., Katzarkov L. V., Mellit A. et al., / Series math "arxiv.org". 2013. No. 1305.4549v1.
A minifold is a smooth projective $n$-dimensional variety such that its bounded derived category of coherent sheaves $\D^b(X)$ admits a semi-orthogonal decomposition into an exceptional collection of $n+1$ exceptional objects. In this paper we classify minifolds of dimension $n \leq 4$. We discuss the structure of the derived category of fake projective spaces and conjecture ...
Added: May 27, 2013
Kochetkov Y., /. 2013. No. 1301.6059.
We consider the space $\mathcal{M}_{2,1}$ --- the open moduli space of complex curves of genus 2 with one marked point. Using language of chord diagrams we describe the cell structure of $\mathcal{M}_{2,1}$ and cell adjacency. This allows one to construct matrices of boundary operators and compute Betty numbers of $\mathcal{M}_{2,1}$ over $\mathbb{Q}$. ...
Added: February 24, 2013