Boson topological insulators: A window into highly entangled quantum phases by Wang, Chong, Todadri, Senthil

“…This includes construction of a time-reversal symmetric SPT state that is not currently part of the cohomology classification of such states.…”
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Significance of Solitonic Fibers in Riemannian Submersions and Some Number Theoretic Applications by Ali H. Hakami, Mohd Danish Siddiqi

“…Finally, we explore some applications of Riemannian submersion along with cohomology, Betti number, and Pontryagin classes in number theory.…”
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Lie Bialgebra Structures on the Lie Algebra <inline-formula><math display="inline"><semantics><mi mathvariant="fraktur">L</mi></semantics></math></inline-formula> Related to the Vi... by Xue Chen, Yihong Su, Jia Zheng

“…It is proved that all such Lie bialgebras are triangular coboundary, and the first cohomology group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>H</mi><mn>1</mn></msup><mo>(</mo><mi mathvariant="fraktur">L</mi><mrow><mo>,</mo><mo> </mo></mrow><mi mathvariant="fraktur">L</mi><mo>⊗</mo><mi mathvariant="fraktur">L</mi><mo>)</mo></mrow></semantics></math></inline-formula> is trivial.…”
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Comments on the quantum field theory of the Coulomb gas formalism by Daniel Kapec, Raghu Mahajan

“…One of these winding operators corresponds to the anti-holomorphic completion of the BRST current first introduced by Felder, and the full left/right cohomology of this BRST charge isolates the irreducible representations of the Virasoro algebra within the degenerate Fock space of the linear dilaton. …”
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Poisson traces, D-modules, and symplectic resolutions by Schedler, Travis, Etingof, Pavel I

“…Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. …”
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Finite Symmetric Integral Tensor Categories with the Chevalley Property with an Appendix by Kevin Coulembier and Pavel Etingof by Etingof, Pavel, Gelaki, Shlomo

“…Finally, we compute the Sweedler cohomology of restricted enveloping algebras over an algebraically closed field $k$ of characteristic $p&amp;gt;0$, classify associators for their duals, and study finite dimensional (not necessarily triangular) local quasi-Hopf algebras and finite (not necessarily symmetric) unipotent tensor categories over an algebraically closed field $k$ of characteristic $p&amp;gt;0$. …”
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Finite dimensional representations of sympletic reflection algebras for wreath products by Montarani, Silvia

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Algebraic topology of manifolds by Hoekzema, R

“…In Chapter 2 I present calculations on the cohomology of the first two Rosenfeld planes, revealing that (O ⊗ C)P² is 2-orientable and (O ⊗ H)P² is at least 3-orientable. …”

On spinc[sic]-invariants of four-manifolds by Leung, W, Leung, Wai-Man Raymond

“…The 'jumping subset' <em>M'</em> defined a cohomology class <em>P</em> of <em>M</em> which is given by the generalised Porteous formula. …”

Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect by Vishwanath, Ashvin, Todadri, Senthil

“…These phases invoke interactions in a fundamental way but do not possess topological order; they are bosonic analogs of free-fermion topological insulators and superconductors. While a formal cohomology-based classification of such states was recently discovered, their physical properties remain mysterious. …”
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Weights of the $\mathbb{F}_{q}$-forms of $2$-step splitting trivectors of rank $8$ over a finite field by M.A. Rakdi, N. Midoune

“….$ The methods of Galois cohomology can be used to determine the classes of nondegenerate trivectors which split into multiple classes when going from $\mathbb{\bar{F}}$ to $\mathbb{F}.$ This program is partially determined by Noui L. and Midoune N. and the classification of trilinear alternating forms on a vector space of dimension $8$ over a finite field $\mathbb{F}_{q}$ of characteristic other than $2$ and $3$ was solved by Noui L. and Midoune N. …”
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Classification of phases for mixed states via fast dissipative evolution by Andrea Coser, David Pérez-García

“…Whereas at the Hamiltonian level, phases are known to be classified with the second cohomology group of the symmetry group, we show that symmetry cannot give any protection in 1D in the Lindbladian sense: there is only one SPT phase in 1D independently of the symmetry group. …”
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Superspace BRST/BV Operators of Superfield Gauge Theories by Ioseph Lvovich Buchbinder, Sylvester James Gates, Konstantinos Koutrolikos

“…<i><b>Q</b></i> acts on the Hilbert space of superfield states, and its cohomology generates the expected superspace equations of motion.…”
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Invariants linked to models of curves over discrete valuation rings by Srinivasan, Padmavathi

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Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow by Joyce, D

“…We conjecture that if $(L,E,b)$ is an object in an enlarged version of $D^b\mathcal F(M)$, where $L$ is a compact, graded Lagrangian in $M$ (possibly immersed, or with "stable singularities"), $E\to M$ a rank one local system, and $b$ a bounding cochain for $(L,E)$ in Lagrangian Floer cohomology, then there is a unique family $\{(L^t,E^t,b^t):t\in[0,\infty)\}$ such that $(L^0,E^0,b^0)=(L,E,b)$, and $(L^t,E^t,b^t)\cong(L,E,b)$ in $D^b\mathcal F(M)$ for all $t$, and $\{L^t:t\in[0,\infty)\}$ satisfies Lagrangian MCF with surgeries at singular times $T_1,T_2,\dots,$ and in graded Lagrangian integral currents we have $\lim_{t\to\infty}L^t=L_1+\cdots+L_n$, where $L_j$ is a special Lagrangian integral current of phase $e^{i\pi\phi_j}$ for $\phi_1&gt;\cdots&gt;\phi_n$, and $(L_1,\phi_1),\ldots,(L_n,\phi_n)$ correspond to the decomposition of $(L,E,b)$ into $(Z,\mathcal P)$-semistable objects. …”

Twistors in curved space time by Mason, L, Mason, Lionel

“…It is shown that certain canonically defined forms on the spin bundle are preferred Dolbeault representatives for derivatives of the twister cohomology classes corresponding to the linearised field.…”

Fibrewise CoHopf spaces by Sunderland, A

“…</p> <p>The Thorn space is used to determine the cohomology ring of the total space of a fibrewise coHopf sphere bundle in terms of that of its base, and a generalised Hopf invariant is constructed which vanishes on fibrewise coHopf sphere bundles.…”

Symmetry-protected topological phases with charge and spin symmetries: Response theory and dynamical gauge theory in two and three dimensions by Ye, Peng, Wang, Juven

“…A large class of symmetry-protected topological phases (SPT) in boson/spin systems have been recently predicted by the group cohomology theory. In this work, we consider bosonic SPT states at least with charge symmetry [U(1) or Z[subscript N]] or spin-S[superscript z] rotation symmetry [U(1) or Z[subscript N]] in two (2D) and three dimensions (3D) and the surface of 3D. …”
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On the homology groups $H_k(\mathbb{C}\Omega_n)$, $k=1, ..., n$ by A.M. Pasko

“…Ruban who in 1985 found the n-dimensional homology group of the space $\Omega_n$ and in 1999 found all the cohomology groups of this space. The spaces $\mathbb{C}\Omega_n$ have been introduced by A.M. …”
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Twisted stable homotopy theory by Douglas, Christopher L

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