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On the rigidity of complex Hirzebruch genera on SU-manifolds
European Journal of Mathematics. 2025. No. 11. Article 27.
Черных Г. С.
We prove that if a complex genus ϕ : U → R is rigid on SU-manifolds with a torus action then ϕ is the elliptic Krichever genus.
Publication based on the results of:
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Batanin M., White D., Journal of Pure and Applied Algebra 2024 Vol. 228 No. 6 Article 107570
Given a combinatorial (semi-)model category M and a set of morphisms C, we establish the existence of a semi-model category LCM satisfying the universal property of the left Bousfield localization in the category of semi-model categories. Our main tool is a semi-model categorical version of a result of Jeff Smith, that appears to be of ...
Added: December 26, 2025
Akhmet’ev P., Switzerland: Springer, 2025.
This book consists of a collection of articles dedicated to Valentin Poénaru, on topology and geometry in a broad sense. Poénaru is one of the leading mathematicians whose work had an essential impact on the development of topology in France over the last forty years of the twentieth century. The special topics addressed in this ...
Added: October 27, 2025
Абрамов А. С., Chernyshev V. L., Mikhaylets E. et al., / Series Social Science Research Network "Social Science Research Network". 2025.
Computer vision is one of the most relevant modern research areas with broad practical applications. However, traditional solutions based on deep learning have signicant limitations and can be misleading. Topological data analysis, on the other hand, is a modern approach to solving similar problems using mathematically deterministic methods of algebraic topology that reduce the risk ...
Added: September 23, 2025
Yunhyung C., Eunjeong L., Mikiya M. et al., Fields Institute Communications 2024 Vol. 89 P. 107–119
Fano Bott manifolds bijectively correspond to signed rooted forests with some equivalence relation. Using this bijective correspondence, we enumerate the isomorphism classes of Fano Bott manifolds and the diffeomorphism classes of indecomposable Fano Bott manifolds. We also observe that the signed rooted forests with the equivalence relation bijectively correspond to rooted triangular cacti. ...
Added: August 30, 2025
Chernyshev V. L., Pyatko D., Математические заметки 2023 Т. 113 № 4 С. 560–576
Получена асимптотика числа конечных положений случайного блуждания на ориентированном гамильтоновом метрическом графе. ...
Added: August 29, 2025
Yunhyung C., Eunjeong L., Mikiya M. et al., Journal of Symplectic Geometry 2023 Vol. 21 No. 3 P. 439–462
We prove that if there exists a c1-preserving graded ring isomorphism between integral cohomology rings of two Fano Bott manifolds, then they are isomorphic as toric varieties. As a consequence, we give an affirmative answer to McDuff’s question on the uniqueness of a toric structure on a Fano Bott manifold. ...
Added: August 29, 2025
Yunhyung C., Eunjeong L., Mikiya M. et al., Proceedings of the Steklov Institute of Mathematics 2025 Vol. 326 P. 339–351
The c1-cohomological rigidity conjecture states that two smooth toric Fano varieties are isomorphic as varieties if there is a c1-preserving isomorphism between their integral cohomology rings. In this paper, we confirm the conjecture for smooth toric Fano varieties of Picard number 2. ...
Added: August 29, 2025
Horiguchi T., Mikiya M., Sato T., Algebraic Combinatorics 2024 Vol. 7 No. 5 P. 1433–1451
The solution of Shareshian-Wachs conjecture by Brosnan-Chow and Guay-Paquet tied the graded chromatic symmetric functions on indifference graphs (or unit interval graphs) and the cohomology of regular semisimple Hessenberg varieties with the dot action. A similar result holds between unicellular LLT polynomials and twins of regular semisimple Hessenberg varieties. A recent result by Abreu-Nigro enabled ...
Added: August 29, 2025
Penskoi A., Karpukhin M., Polterovich I. et al., , in: Surveys in Differential Geometry. Volume 24 (2019).Vol. 24: Differential geometry, Calabi-Yau theory, and general relativity.: International Press of Boston Inc, 2019.
The paper is concerned with the maximization of Laplace eigenvalues on surfaces of given volume with a Riemannian metric in a fixed conformal class. A significant progress on this problem has been recently achieved by Nadirashvili–Sire and Petrides using related, though different methods. In particular, it was shown that for a given , the maximum of ...
Added: January 31, 2025
International Press of Boston Inc, 2019.
Added: January 31, 2025
Panov T., М.: МЦНМО, 2024.
Настоящее издание подготовлено на основе лекционных курсов «Введение в топологию», «Топология-1», «Топология-2» и «Теория гомологий», прочитанных автором на механико-математическом факультете МГУ, в Независимом московском университете и Новосибирском университете.
В первой части рассматриваются основы теории гомотопий: клеточные пространства, фундаментальная группа, накрытия, гомотопическая теория расслоений и высшие гомотопические группы.
Во вторую часть входит теория гомологий: симплициальные, сингулярные и клеточные ...
Added: January 15, 2025
Springer, 2024.
This book explores toric topology, polyhedral products and related mathematics from a wide range of perspectives, collectively giving an overview of the potential of the areas while contributing original research to drive the subject forward in interesting new directions. Contributions to this volume were written in connection to the thematic program Toric Topology and Polyhedral Products held ...
Added: January 15, 2025
Petr E Brandyshev, Yury A Budkov, Journal of Statistical Mechanics: Theory and Experiment 2023 No. 12 Article 123206
In this paper, we introduce a statistical field theory that describes the macroscopic mechanical forces in inhomogeneous Coulomb fluids. Our approach employs the generalization of Noether's first theorem for the case of a fluctuating order parameter to calculate the stress tensor for Coulomb fluids. This tensor encompasses the mean-field stress tensor and fluctuation corrections derived ...
Added: December 18, 2023
Ayzenberg A., Beketov M., Magaj G., / Series arxiv:math.AT "arxiv Algebraic Topology". 2023.
In this paper we study the nerves of two types of coverings of a sphere $S^{d-1}$: (1) coverings by open hemispheres; (2) antipodal coverings by closed hemispheres. In the first case, nerve theorem implies that the nerve is homotopy equivalent to $S^{d-1}$. In the second case, we prove that the nerve is homotopy equivalent to ...
Added: October 5, 2023
Brandyshev P., Budkov Y., Journal of Chemical Physics 2023 Vol. 158 No. 17 Article 174114
In this paper, we present a covariant approach that utilizes Noether’s second theorem to derive a symmetric stress tensor from the grand thermodynamic potential functional. We focus on the practical case where the density of the grand thermodynamic potential is dependent on the first and second coordinate derivatives of the scalar order parameters. Our approach ...
Added: May 5, 2023
Nikolay Konovalov, / Series "Working papers by Cornell University". 2022. No. 2209.03312.
Let $\mathsf{s}_0\mathsf{Lie}^r$ be the category of $0$-reduced simplicial restricted Lie algebras over a fixed perfect field of positive characteristic $p$. We prove that there is a full subcategory $\mathrm{Ho}(\mathsf{s}_0\mathsf{Lie}^r_{\xi})$ of the homotopy category $\mathrm{Ho}(\mathsf{s}_0\mathsf{Lie}^r)$ and an equivalence $\mathrm{Ho}(\mathsf{s}_0\mathsf{Lie}^r_{\xi})\simeq\mathrm{Ho}(\mathsf{s}_1\mathsf{CoAlg}^{tr})$. Here $\mathsf{s}_1\mathsf{CoAlg}^{tr}$ is the category of $1$-reduced simplicial truncated coalgebras; informally, a coaugmented cocommutative coalgebra $C$ is ...
Added: September 12, 2022
Nikolai Konovalov, / Series "Working papers by Cornell University". 2020. No. 2010.09097.
In this note we compare the fracture squares from genuine equivariant stable homotopy theory and the fracture squares which appear in the Goodwillie tower for the norm functor. ...
Added: September 12, 2022
Gavrilovich M., Pimenov K., / Series math "arxiv.org". 2020.
We interpret a construction of geometric realisation by [Besser], [Grayson], and [Drinfeld] of a simplicial set as constructing a space of maps from the interval to a simplicial set, in a certain formal sense, reminiscent of the Skorokhod space of semi-continuous functions; in particular, we show the geometric realisation functor factors through an endofunctor of ...
Added: October 29, 2020