Results 1 to 10 of about 10,908 (98)
Mathematical Models of Abstract Systems: Knowing abstract geometric forms [PDF]
, 2013 Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they ...
Marquis, Jean-Pierre
core +3 more sources
Coassembly is a homotopy limit map
, 2020 We prove a claim by Williams that the coassembly map is a homotopy limit map. As an application, we show that the homotopy limit map for the coarse version of equivariant $A$-theory agrees with the coassembly map for bivariant $A$-theory that appears in ...
Malkiewich, Cary, Merling, Mona
core +1 more source
The T-algebra spectral sequence: Comparisons and applications [PDF]
, 2014 In previous work with Niles Johnson the author constructed a spectral sequence for computing homotopy groups of spaces of maps between structured objects such as G-spaces and E_n-ring spectra.
Noel, Justin
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Subdivision-based homotopy equivalence of digital circles
Applied General TopologyA direct translation of the notion of homotopy equivalence from algebraic topology to digital images leads to a much more rigid definition in the context of digital topology. This results in two digital circles of different radii being not homotopic.
Samia Ashraf +2 more
doaj +1 more source
Units of ring spectra and their traces in algebraic K-theory
, 2004 Let GL_1(R) be the units of a commutative ring spectrum R. In this paper we identify the composition BGL_1(R)->K(R)->THH(R)->\Omega^{\infty}(R), where K(R) is the algebraic K-theory and THH(R) the topological Hochschild homology of R.
Schlichtkrull, Christian
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Moduli stacks of algebraic structures and deformation theory [PDF]
, 2015 We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate diagram category ...
Yalin, Sinan
core +1 more source
The localization sequence for the algebraic K-theory of topological K-theory
, 2006 We prove a conjecture of Rognes by establishing a localization cofiber sequence of spectra, K(Z) to K(ku) to K(KU) to Sigma K(Z), for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a devissage
Andrew J. Blumberg +4 more
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Rigidification of algebras over multi-sorted theories
, 2009 We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result for simplicial algebras over these theories, showing that there is a
Adámek +13 more
core +1 more source
Product and other fine structure in polynomial resolutions of mapping spaces
, 2002 Let Map_T(K,X) denote the mapping space of continuous based functions between two based spaces K and X. If K is a fixed finite complex, Greg Arone has recently given an explicit model for the Goodwillie tower of the functor sending a space X to the ...
Adams +11 more
core +2 more sources
Calculus of functors and model categories II [PDF]
, 2014 This is a continuation, completion, and generalization of our previous joint work with B. Chorny. We supply model structures and Quillen equivalences underlying Goodwillie's constructions on the homotopy level for functors between simplicial model ...
Biedermann, Georg, Röndigs, Oliver
core +1 more source