Jos\'e M. Moreno-Fern\'andez, Bruno Stonek Algebraic models for equivariant rational homotopy theory for discrete groups https://arxiv.org/abs/2601.17345

Arpon Raksit Notes on Tate cohomology https://arxiv.org/abs/2601.17677

Vidit Nanda, Francesca Tombari Stratified Morse Theory for Cell Complexes https://arxiv.org/abs/2601.18343

Semyon Abramyan Graphical composition of mapping spaces between modules of configuration-space-type https://arxiv.org/abs/2601.18363

Jonathan Buchanan, Arun Debray, Cameron Krulewski, Stephen McKean Hyperk\"ahler bases for six rational bordism theories https://arxiv.org/abs/2601.18701

Taito Shimoji Quasi-projective nilmanifolds https://arxiv.org/abs/2601.16433

Mujtaba Ali, Tom Needham, Anastasios Stefanou, Ling Zhou On the Hausdorff stability of barcodes over posets https://arxiv.org/abs/2601.16947

Euan Aitken Equivariant linear isometries and infinite little discs operads via transfer systems https://arxiv.org/abs/2601.15800

Zhen Huan 2-Equivariant 2-Vector bundles and 2K-theories https://arxiv.org/abs/2601.15893

Jose Manuel Garcia Calcines, Jose Antonio Vilches Alarcon Bivariate topological complexity: a framework for coordinated motion planning https://arxiv.org/abs/2601.16059

Marco Praderio Bova Computing higher limits over the fusion orbit category via amalgams https://arxiv.org/abs/2601.14983

Sacha Goldman The Torsion of Automorphisms of Nilpotent Spaces https://arxiv.org/abs/2601.14988

Bala Krishnamoorthy, Elizabeth Thompson A Stable Measure of Chaos in Dynamical Systems Using Persistent Homology https://arxiv.org/abs/2601.10900

Jiaxi Zha Topological CoHochschild Homology and Thom Spectra https://arxiv.org/abs/2601.11263

Jes\'us A. \'Alvarez L\'opez, Alejandro O. Majadas-Moure New Applications and Computations of the Lefschetz Number of Homeomorphisms and Open Maps https://arxiv.org/abs/2601.11370

Jake Cordes, Barbara Giunti, Zheng Wu SuPerPoV: Score and evolution of the stratospheric polar vortex via persistent homology https://arxiv.org/abs/2601.11386

Trygve Poppe Oldervoll Quasi-unitial Inner Kan Spaces https://arxiv.org/abs/2601.11489

Astrid A. Olave, Elizabeth Munch Bounding the interleaving distance on concrete categories using a loss function https://arxiv.org/abs/2601.09034

Jo\~ao Candeias, Javier J. Guti\'errez A new model structure on dendroidal spaces for the theory of $\infty$-operads https://arxiv.org/abs/2601.09505

Alexey G. Gorinov, Alexander V. Zakharov Binomial rings, and integral homology of complements of compact toric arrangements https://arxiv.org/abs/2601.07902

William Balderrama, Piotr Pstr\k{a}gowski Unstable synthetic deformations I: Malcev theories https://arxiv.org/abs/2601.08802

William Balderrama, Piotr Pstr\k{a}gowski Unstable synthetic deformations II: Infinitesimal extensions https://arxiv.org/abs/2601.08812

Ramandeep Singh Arora, Sutirtha Datta, Navnath Daundkar, Gopal Chandra Dutta On the $m$-dimensional sectional category and induced invariants https://arxiv.org/abs/2601.05334

Shiquan Ren Homological obstructions for regular embeddings of graphs https://arxiv.org/abs/2601.05479

Martin Bendersky, Robert Thompson $K$-Bad Spheres https://arxiv.org/abs/2601.02620

Damjan Pi\v{s}talo Homotopical algebra of Lie-Rinehart pairs https://arxiv.org/abs/2601.02895

Samik Basu, Vanny Doem, Chandal Nahak Rational stable homotopy type of equivariant projective spaces and Grassmannians https://arxiv.org/abs/2601.02940

Victor Roca i Lucio, Dan Petersen, Sinan Yalin Point-set models for homotopy coherent coalgebras https://arxiv.org/abs/2601.03101

Kazuhiro Kawamura, Sushovan Majhi, Atish Mitra The Shadow of Vietoris--Rips Complexes in Limits https://arxiv.org/abs/2601.01359

Joana Cirici On the real homotopy type of compact complex surfaces https://arxiv.org/abs/2601.01958

Ruizhi Huang Homotopy of Simply Connected Complexes with a Spherical Pair https://arxiv.org/abs/2601.02247

Michael Usher Filtered cospans and interlevel persistence with boundary conditions https://arxiv.org/abs/2512.24025

Minkyu Kim Polynomial functors over free nilpotent groups https://arxiv.org/abs/2512.24048

Sophia E Marx, Rajan Amit Mehta Coherent span-valued 2D TQFTs https://arxiv.org/abs/2512.24887

Sel\c{c}uk Kayacan Persistent Homology via Finite Topological Spaces https://arxiv.org/abs/2512.23348

Jyh-Haur Teh The asphericity of locally finite infinite configuration spaces and Weierstrass entire coverings https://arxiv.org/abs/2512.21498

Rafael Cavalcanti Geometric Obstructions in Finsler Spaces and Torsion-Free Persistent Homology https://arxiv.org/abs/2512.22079

M\'aria \v{S}imkov\'a Rational Homotopy Equivalence https://arxiv.org/abs/2512.21182

Manas Mandal, Divya Setia Rational Cohomology Endomorphisms of Product of Sphere with Grassmannian and Coincidence Theory https://arxiv.org/abs/2512.21305

Florian De Leger A combinatorial approach to Kontsevich's Swiss cheese conjecture https://arxiv.org/abs/2512.20167

Geoffrey Powell Cyclic operads, Koszul complexes, and hairy graph complexes https://arxiv.org/abs/2512.20256

Geoffrey Powell Operads, modules over walled Brauer categories, and Koszul complexes https://arxiv.org/abs/2512.20274

Christian Carrick, Bertrand Guillou, Sarah Petersen The real Brown-Peterson homology of $\Omega^\rho S^{\rho + 1}$ https://arxiv.org/abs/2512.18019

Alba Send\'on Blanco Cobordism of nested manifolds https://arxiv.org/abs/2512.18277

Benjamin Br\"uck, Jeremy Miller, Kevin Ivan Piterman An analogue of Rognes' connectivity conjecture for free groups https://arxiv.org/abs/2512.19128

Fei Han, Ruizhi Huang, Weiping Zhang An Almost Flat Spin$^c$ Manifold Bounds https://arxiv.org/abs/2512.19335

Mark Grant Secondary cohomology operations and sectional category https://arxiv.org/abs/2512.19461

Luigi Caputi, Francesco Vaccarino Diagrammatic Hochschild cohomology via cohomology of categories, and incidence algebras https://arxiv.org/abs/2512.15835

Jesse Keyes, Jordan Sawdy Picard Groups in Equivariant Algebra and Stable Homotopy Theory https://arxiv.org/abs/2512.16002

Kensuke Arakawa, Victor Carmona, Francesca Pratali Relative operads model $\infty$-operads https://arxiv.org/abs/2512.16374