Topology of CW complexes/ by 176435 Lundell, Albert T.

A Cheeger-Buser-type inequality on CW complexes by Grégoire Schneeberger

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The homology groups $H_{n+1} \left( \mathbb{C}\Omega_n \right)$ by A.M. Pasko

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Minimum d-convex partition of a multidimensional polyhedron with holes by Ion Băţ

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Morse theory for C*-algebras: a geometric interpretation of some noncommutative manifolds by Vida Milani, Ali Asghar Rezaei, Seyed M.H. Mansourbeigi

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MIXED SERRE FIBRATION by Zahraa Yassin Habeeb, Daher Al Baydli

Subjects: “…M-Serre fibration, CW-complex space, M-path lifting property, M-Covering Homotopy Property.…”
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Discrete Morse theory and localization by Nanda, V

“…Incidence relations among the cells of a regular CW complex produce a poset-enriched category of entrance paths whose classifying space is homotopy-equivalent to that complex. …”

Discrete Morse theory and classifying spaces by Nanda, V, Tamaki, D, Tanaka, K

“…To an acyclic partial matching μ on a finite regular CW complex X, Forman introduced a discrete analogue of gradient flows. …”

Rational homotopy nilpotency of self-equivalences by Salvatore, P

“…We study the homotopy nilpotency, after rationalization, of some spaces of self-homotopy equivalences of a finite, simply connected CW-complex.…”

The Ball-Based Origami Theorem and a Glimpse of Holography for Traversing Flows by Katz, Gabriel

“…The CW-complex $$\mathcal T(v)$$T(v) captures some residual information about the smooth structure on X (such as the stable tangent bundle of X). …”
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Local cohomology and stratification by Nanda, V

“…We outline an algorithm to recover the canonical (or, coarsest) stratification of a given finite-dimensional regular CW complex into cohomology manifolds, each of which is a union of cells. …”

Combinatorial Topology of Toric arrangements by Giacomo d'Antonio, Emanuele Delucchi

“…We prove that the complement of a complexified toric arrangement has the homotopy type of a minimal CW-complex, and thus its homology is torsion-free. To this end, we consider the toric Salvetti complex, a combinatorial model for the arrangement's complement. …”
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Cuts and Flows of Cell Complexes by Art M. Duval, Caroline J. Klivans, Jeremy L. Martin

“…We study the vector spaces and integer lattices of cuts and flows of an arbitrary finite CW complex, and their relationships to its critical group and related invariants. …”
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Some problems in algebraic topology by Gilbert, W

“…THEOREM Let A be countable CW-complex, then $cocat A geq wcocat A geq nil A geq W-long A$ and furthermore all the inequalities can occur. …”

Infinite loop spaces and nilpotent K-theory by Adem, A, Gomez, J, Lind, J, Tillmann, U

“…We introduce the notion of q-nilpotent K-theory of a CW-complex X for any q ≥ 2, which extends the notion of commutative K-theory defined by Adem-G´omez, and show that it is represented by Z × B(q, U), were B(q, U) is the q-th term of the aforementioned filtration of BU. …”

Homotopy properties of horizontal loop spaces and applications to closed sub-riemannian geodesics by Lerario, A, Mondino, A

“…In particular we prove that $\Lambda$ (with the $W^{1,2}$ topology) has the homotopy type of a CW-complex, that its inclusion in the standard base-point free loop space (i.e. the space of loops with no non-holonomic constraint) is a homotopy equivalence, and consequently its homotopy groups can be computed as $\pi_k(\Lambda)\simeq \pi_k(M) \ltimes \pi_{k+1}(M)$ for all $k\geq 0.$ These topological results are applied, in the second part of the paper, to the problem of the existence of closed sub-riemannian geodesics. …”