Results 11 to 20 of about 333 (49)
Cone‐equivalent nilpotent groups with different Dehn functions
Proceedings of the London Mathematical Society, Volume 126, Issue 2, Page 704-789, February 2023., 2023 Abstract For every k⩾3$k\geqslant 3$, we exhibit a simply connected k$k$‐nilpotent Lie group Nk$N_k$ whose Dehn function behaves like nk$n^k$, while the Dehn function of its associated Carnot graded group gr(Nk)$\mathsf {gr}(N_k)$ behaves like nk+1$n^{k+1}$. This property and its consequences allow us to reveal three new phenomena.
Claudio Llosa Isenrich +2 more
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Journal of the London Mathematical Society, Volume 106, Issue 2, Page 590-661, September 2022., 2022 Abstract Given a generic stable strongly parabolic SL(2,C)$\operatorname{SL}(2,\mathbb {C})$‐Higgs bundle (E,φ)$({\mathcal {E}}, \varphi )$, we describe the family of harmonic metrics ht$h_t$ for the ray of Higgs bundles (E,tφ)$({\mathcal {E}}, t \varphi )$ for t≫0$t\gg 0$ by perturbing from an explicitly constructed family of approximate solutions ...
Laura Fredrickson +3 more
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Some recent advances in topological Hochschild homology
Bulletin of the London Mathematical Society, Volume 54, Issue 1, Page 1-44, February 2022., 2022 Abstract We give an account of the construction of the Bhatt–Morrow–Scholze motivic filtration on topological cyclic homology and related invariants, focusing on the case of equal characteristic p$p$ and the connections to crystalline and de Rham–Witt theory.
Akhil Mathew
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Homotopy type of the complex of free factors of a free group
Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1737-1765, December 2020., 2020 Abstract We show that the complex of free factors of a free group of rank n⩾2 is homotopy equivalent to a wedge of spheres of dimension n−2. We also prove that for n⩾2, the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is (n−2)‐connected.
Benjamin Brück, Radhika Gupta
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Connection space approach to ambiguities of gauge theories
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 15, Page 2365-2371, 2005., 2005 Two distinct gauge potentials can have the same field strength, in which case they are said to be “copies” of each other. The consequences of this ambiguity for the general affine space 𝒜 of gauge potentials are examined. Any two potentials are connected by a straight line in 𝒜, but a straight line going through two copies either contains no other copy
R. Aldrovandi, A. L. Barbosa
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Moduli space of filtered λ‐ringstructures over a filtered ring
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 39, Page 2065-2084, 2004., 2004 Motivated in part by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered λ‐ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this set has a canonical topology compatible with the filtration on the given filtered ring.
Donald Yau
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On ideals and homology in additive categories
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 8, Page 439-451, 2002., 2002 Ideals are used to define homological functors in additive categories. In abelian categories the ideals corresponding to the usual universal objects are principal, and the construction reduces, in a choice dependent way, to homology groups. The applications considered in this paper are: derived categories and functors.
Lucian M. Ionescu
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Holomorphic field theories and higher algebra
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
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Homological Lie brackets on moduli spaces and pushforward operations in twisted K‐theory
Journal of Topology, Volume 18, Issue 2, June 2025.Abstract We develop a general theory of pushforward operations for principal G$G$‐bundles equipped with a certain type of orientation. In the case G=BU(1)$G={B\mathrm{U}(1)}$ and orientations in twisted K‐theory, we construct two pushforward operations, the projective Euler operation, whose existence was conjectured by Joyce, and the projective rank ...
Markus Upmeier
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Orbifold Kodaira–Spencer maps and closed‐string mirror symmetry for punctured Riemann surfaces
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract When a Weinstein manifold admits an action of a finite abelian group, we propose its mirror construction following the equivariant 2D TQFT‐type construction, and obtain as a mirror the orbifolding of the mirror of the quotient with respect to the induced dual group action. As an application, we construct an orbifold Landau–Ginzburg mirror of a
Hansol Hong, Hyeongjun Jin, Sangwook Lee
wiley +1 more source