Tootfinder

Universal Assembly and Cellular Loop Spaces on Regular CW Complexes
Serhii Dylda, Tibor Macko
https://arxiv.org/abs/2606.05051 https://arxiv.org/pdf/2606.05051 https://arxiv.org/html/2606.05051
arXiv:2606.05051v1 Announce Type: new
Abstract: We develop a regular CW analogue of the classical assembly formalism for chain complexes appearing in algebraic surgery theory. From the cell poset, we construct combinatorial path and loop objects using fences of comparable cells and prove that their classifying spaces recover the homotopy types of the ordinary based path and loop spaces. The resulting loop object carries a natural monoid structure, giving rise to a DG algebra defined directly from the cellular structure.
For complexes of cellular cosheaves, we introduce a universal assembly functor to modules over the group ring of the fundamental group and study the localization determined by global equivalences. The associated homotopy category is identified with a Verdier quotient of the derived category of cellular cosheaves, and its fibrant objects are precisely the homotopy locally constant complexes. A single elementary cosheaf becomes a compact generator after localization, and its derived endomorphism DG algebra is identified with singular chains on the cellular loop space. Consequently, the localized theory admits a Morita description in terms of DG modules over the loop DG algebra. The formalism provides a regular CW counterpart of the classical delta-set approach to assembly in algebraic surgery theory due to Ranicki and Weiss.
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Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[5/5]:
- Energy-Modulated Time-Asymmetric Spontaneous Collapse: Forward-Backward Dynamics from Stochastic ...
Ikechukwu C. Okoro, Mike O. Osiele, Godfrey E. Akpojotor
https://arxiv.org/abs/2606.06452 https://mastoxiv.page/@arXiv_quantph_bot/116696558215965415
- Fun with Graph States: Nonlocal Bell Pairs and the Arf Invariant
Bartlomiej Czech, Yichen Feng, Xianlai Wu, Minjun Xie
https://arxiv.org/abs/2606.06582 https://mastoxiv.page/@arXiv_quantph_bot/116713369377389218
- JGRA: Jacobian Geometry Robustness Assessment in NISQ Noise-Aware Quantum Neural Networks
Gianluca Scanu, Luca Barletta, Stefano Rini
https://arxiv.org/abs/2606.09964 https://mastoxiv.page/@arXiv_quantph_bot/116724737493129996
- Towards the implementation of a quantum classifier
Lorenzo Confalonieri
https://arxiv.org/abs/2606.10150 https://mastoxiv.page/@arXiv_quantph_bot/116724826333574245
- Classical representation of the dynamics of quantum spin chains
Tony Jin
https://arxiv.org/abs/2502.10502 https://mastoxiv.page/@arXiv_condmatstatmech_bot/114023643712493871
- A Physics-Inspired Optimizer: Velocity Regularized Adam
Pranav Vaidhyanathan, Lucas Schorling, Natalia Ares, Maike Osborne
https://arxiv.org/abs/2505.13196 https://mastoxiv.page/@arXiv_csLG_bot/114539123804911573
- TensorKit.jl: A Julia package for large-scale tensor computations, with a hint of category theory
Lukas Devos, Jutho Haegeman
https://arxiv.org/abs/2508.10076 https://mastoxiv.page/@arXiv_csMS_bot/115031801387098178
- Magneto-Optical Trapping of a Metal Hydride Molecule
Jinyu Dai, Benjamin Riley, Qi Sun, Debayan Mitra, Tanya Zelevinsky
https://arxiv.org/abs/2512.22350 https://mastoxiv.page/@arXiv_physicsatomph_bot/115807661192131547
- Integrable Massless and Massive Fermions
Zhao Zhang
https://arxiv.org/abs/2603.11172 https://mastoxiv.page/@arXiv_nlinSI_bot/116220764978246106
- Holographic Complexity, Extremality, and Cosmic Censorship
Fuat Berkin Altunkaynak
https://arxiv.org/abs/2604.20170 https://mastoxiv.page/@arXiv_hepth_bot/116453018510714885
- Strong-field control of the $Z$-boson resonance in $e^ e^-$ collisions
Fengye Chen, Qingzheng Lv, Libin Fu
https://arxiv.org/abs/2606.09394 https://mastoxiv.page/@arXiv_hepph_bot/116719301448440291
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Burklund-Lin-Wang-Xu Methods in the Cofiber-of-Tau Formalism and Applications to Equivariant Slice Differentials
Yuchen Wu
https://arxiv.org/abs/2606.02779 https://arxiv.org/pdf/2606.02779 https://arxiv.org/html/2606.02779
arXiv:2606.02779v1 Announce Type: new
Abstract: We reinvestigate the theory of spectral sequences by studying the $(\infty,1)$-category of filtered spectra through the cofiber-of-$\tau$ formalism of Burklund-Isaksen-Pstragowski-Wang-Xu. In this framework, we define and analyze hidden extensions along arbitrary maps of filtered spectra, establishing computational principles that extend the generalized Leibniz rule and the generalized Mahowald trick of Lin-Wang-Xu, as well as Burklund's Leibniz rule for total differentials, from the Adams spectral sequence to this broader setup. Our formulation uses a more refined, layered notion of extension, which slightly sharpens these statements even for the Adams spectral sequence. As an application, we study equivariant slice spectral sequences and obtain new families of "exotic transfer" differentials in the $C_4$-slice spectral sequences for the Hill-Hopkins-Ravenel theories $\mathrm{BP}^{((C_4))}\langle m\rangle$ for every $m \ge 1$.
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