<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        Stack Exchange Network

        Stack Exchange network consists of 174 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

        Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras

        6
        votes
        1answer
        100 views

        Example of nonvanishing Waldhausen Nil group

        In a remarkable series of papers, both anticipating development in geometric topology and algebraic K-theory, specifically what we call now the Farrell-Jones conjecture, Waldhausen ...
        18
        votes
        1answer
        175 views

        To what extent can we characterise the image of the topological Chern character?

        For a finite CW complex $X$, the Chern character gives an isomorphism of finite-dimensional vector spaces: $$ ch : K^*(X)\otimes \mathbb{Q} \to H^*(X, \mathbb{Q}). $$ The vector space $V = H^*(X, \...
        7
        votes
        0answers
        96 views

        Torsion in Atiyah Singer index formula

        In the papers of Atiyah and Singer, they first show their index theorem and then derive some index formulas. For the Fredohlm index living in the integers, they use the fact that on spheres the Chern ...
        12
        votes
        1answer
        494 views

        Reference for the algebro-geometric proof of Matsumoto theorem

        Matsumoto proved in his PhD thesis that if $F$ is a field then $$K_2(F)=(F^*\otimes F^*)/(x\otimes (1-x)).$$ The original Matsumoto proof as it is written in Milnor's book on algebraic K-theory looks ...
        7
        votes
        0answers
        147 views

        Does Deligne's exceptional series lead to an “exceptional K-theory”?

        To a certain extent, Deligne's exceptional series $A_1 \subset A_2 \subset G_2 \subset D_4 \subset F_4 \subset E_6 \subset E_7 \subset E_8$ plays a role analogous to the classical series $A_n \subset ...
        31
        votes
        0answers
        333 views

        Chern character of a Representation

        Let $G$ be a finite group. Under the identification of the representation ring $R_{\mathbb{C}}(G)$ with the equivariant K-theory $KU^0_G(\ast)$ of the point, followed by Atiyah-Segal completion-...
        17
        votes
        1answer
        285 views

        Milnor Conjecture on Lie groups for Morava K-theory

        A conjecture by Milnor state that if $G$ is a Lie group, then the map $B(G^{disc})\to BG$ sending the classifying space of $G$ endowed with the discrete topology to the classifying space of the ...
        3
        votes
        0answers
        76 views

        Twisted spin cobordism v.s. KO theory in low dimensions

        Based on the background info and this this webpage, here is a more advanced problem: Question: If we consider a different more subtle twisted structure, like $${\Omega_d^{(\mathrm{spin} \times G)/N}},...
        7
        votes
        1answer
        224 views

        Spin cobordism v.s. KO theory in low or in any dimensions

        It seems that from this webpage, the spin cobordism is equivalent to KO theory in low dimension. If we denote the $p$-torsion part (mean $\mathbb{Z}_{p^n}$ for some $n$) $$\Omega_d(BG)_p.$$ ...
        1
        vote
        2answers
        104 views

        Why is the flat cotorsion pair actually a cotorsion pair?

        I asked this question some while ago on Stack Exchange but didn't get an answer (link), so I am trying it here as well. Fix a ringed space $(X,\mathcal{O})$ and denote by $\mathcal{F}$ the class of ...
        8
        votes
        0answers
        211 views

        Is there a citeable source for generators and relations of simplicial sets?

        Simplicial sets can be specified using generators and relations, in complete analogy with groups, rings, etc. More precisely, a system of generators of relations for a simplicial set consists of a ...
        3
        votes
        0answers
        77 views

        About mod 2 Index of Dirac Operators in 3D on Non-Orientable Manifold

        I was reading Witten's paper "Fermion Path Integrals and Topological Phases" (https://arxiv.org/abs/1508.04715). He claimed that Indeed, on an orientable 3-manifold, the eigenvalues of the Dirac ...
        5
        votes
        1answer
        177 views

        Are these two constructions of $K_0(A)$ isomorphic?

        The following question is extracted from this question on MSE, which got no answer so far, probably because it was a bit hidden by another question which a posteriori was totally obvious. Let $A$ be ...
        3
        votes
        1answer
        212 views

        Is Quillen's bracket a “universal enveloping” something?

        $\newcommand{\G}{\mathcal{G}}$ In K-theory, there is a construction due to Quillen as follows. Let $(\G, \oplus, 0)$ be a monoidal groupoid. Then the bracket $\langle \G, \G \rangle$, sometimes also ...
        1
        vote
        0answers
        33 views

        Functoriality in the group $G$ of the domain of the Baum-Connes map

        Lück claims in his preliminary book, that the left hand side of the Baum-Connes map is functorial in the group $G$. For the right hand side $K(A \rtimes G)$ this is clear for the full crossed product, ...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>