<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Stack Exchange Network

      Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

      Visit Stack Exchange

      Questions tagged [homotopy-theory]

      Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.

      3
      votes
      0answers
      77 views

      $\infty$-categorical understanding of Bridgeland stability conditions?

      On triangulated categories we have a notion of Bridgeland stability conditions. Is there any known notion of "derived stability conditions" on a stable $\infty$ category $C$ such that they become ...
      1
      vote
      0answers
      59 views

      A homotopy problem for morphisms of dg-algebras

      Let $\mathfrak g$ be a real finite-dimensional Lie algebra, and suppose we are given two morphisms of dg-algebras $f,g: (C^\bullet(\mathfrak g),d_{CE}) \to (\Omega^\bullet(\Delta^n),d)$, such that ...
      7
      votes
      2answers
      368 views

      What are the advantages of simplicial model categories over non-simplicial ones?

      Of course, there are general results allowing one to replace a model category with a simplicial one. But suppose I want to stay in my original non-simplicial model category (say for some reason I'm a ...
      6
      votes
      0answers
      120 views

      Does Ex^∞ send homotopy inverse limits of ∞-categories to homotopy inverse limits of spaces

      Kan's functor $\operatorname{Ex}^{\infty}$ plays the role of total localization or groupoid completion in the theory of $\infty$-categories; specifically, it can be viewed as the left-adjoint of the ...
      1
      vote
      1answer
      90 views

      The table reduction morphism of operads from Barratt-Eccles to Surjection

      The Barratt-Eccles operad $E$ in the category of simplicial sets is obtained by applying the nerve functor to the canonical operad $\{\Sigma_n\}_{n>0}$ in groups. Berger-Fresse defined here an ...
      8
      votes
      2answers
      288 views

      Iterated free infinite loop spaces

      Let $Q$ denote $\Omega^\infty\circ \Sigma^\infty$ the free infinite loop space functor. Given some space $X$, we see that $QX$ carries all the stable homotopy information about $X$. Naturally I wanted ...
      7
      votes
      0answers
      162 views

      Construction of a $K(\pi,1)$-space?

      My colleague suggested a proof of a fact which I have hard time to believe. Since I am not a topologist by training I am asking it here. Consider any CW-complex structure on the $d$-dimensional ...
      6
      votes
      1answer
      100 views

      Two models for the classifying space of a subgroup via the geometric bar construction

      Let $H$ be a topological group which is a subgroup of two other topological groups $G$ and $G'$. It follows (from Rmk 8.9 in May - Classifying spaces and fibrations (MSN, free)) that there exist weak ...
      6
      votes
      0answers
      95 views

      Extension of sheaves of $\infty$-algebras

      Let $(\mathcal{C},\tau)$ be a site, whose Grothendieck topology is $\tau$ $F : \mathcal{C}\to D(k)$ a sheaf of $\infty$-$k$-algebras, with $k$ a ring and $D(k)$ the derived category of $k$-modules. ...
      3
      votes
      0answers
      39 views

      Tensor product of an L-infinity algebra with the cochains on the 1-simplex

      I would like to understand the $L_\infty$ structure on the tensor product of an $L_\infty$ algebra (over $\mathbb{R}$) $L$ with the normalized cochains on the one-simplex $N^*(\Delta^1)$. This latter ...
      4
      votes
      0answers
      109 views

      References on $HZR$ theory

      Are there references available on $HZR$ theory ? I found on ncatlab that this is "genuinely $\mathbb Z/ 2\mathbb{Z}$-equivariant cohomology version of ordinary cohomology" Found nothing on wikipedia,...
      8
      votes
      0answers
      165 views

      $\Gamma$-sets vs $\Gamma$-spaces

      I know that every $\Gamma$-space is stably equivalent to a discrete $\Gamma$-space, i.e. a $\Gamma$-set. For example, Pirashvili proves, as theorem 1.2 of Dold-Kan Type Theorem for $\Gamma$-Groups, ...
      10
      votes
      1answer
      715 views

      Homology of the fiber

      Let $f:X\rightarrow Y $ be a fibration (with fiber $F$) between simply connected spaces such that $H_{\ast}(f):H_{\ast}(X,\mathbb{Z})\rightarrow H_{\ast}(Y,\mathbb{Z})$ is an isomorphism for $\ast\...
      2
      votes
      1answer
      137 views

      $X \rtimes Y \simeq X \vee (X \wedge Y)$ for $X$ a co-H-Space

      I have asked the below question on MathSE (with a 200 point bounty) but have yet to receive an answer there, and so am trying here. I am happy to remove it if it is nevertheless decided that this ...
      0
      votes
      0answers
      132 views

      Defining a graded ring structure on $\bigoplus_{i} \text{Ext}^i (A,A)$

      I read that, using the fact that $\text{Tot}^{\prod}(\text{Hom}(P_{\bullet} ,Q_{\bullet}))$ can by used to compute $\text{Ext}^* (A,B)$ (which I understand), we can give $\bigoplus_{i} \text{Ext}^i (A,...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>