<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

        Questions tagged [cobordism]

        Cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold.

        8
        votes
        1answer
        363 views

        Critical dimensions D for “smooth manifolds iff triangulable manifolds”

        I am aware that at least for lower dimensions, "smooth manifolds iff triangulable manifolds" at least for dimensions below a certain critical dimensions D. My question is that for ...
        6
        votes
        1answer
        192 views

        Are there non trivial maps from $H\mathbb{Z}$ to $MGL$?

        Let $k$ be a field of characteristic $0$. Let us denote by $\mathbf{1}_{k}$ the sphere spectrum. Let $MGL$ be the algebraic cobordism spectrum. We have the following diagram $$H\mathbb{Z}\...
        4
        votes
        0answers
        65 views

        Decomposition of bordism groups for $BG$ where $G$ is a product of two groups

        Let a group $G=G_1 \times G_2$, where $G_1$ is a discrete group (can be finite or infinite), $G_2$ be any compact Lie group or finite group. Question: Is there some simple result that we can ...
        5
        votes
        0answers
        128 views

        Categorification-like statement in the cobordism group?

        Suppose we consider a $d$-cobordism group classifying manifolds with $H$-structure and with a classifying space $BG$ of a group $G$, written as $$ \Omega^{d}_{H}(BG)= \mathbb{Z}_m \oplus \dots, $$ ...
        6
        votes
        0answers
        103 views

        Pin cobordism v.s. “KO” theory in low or in any dimensions

        Fact: The spin cobordism is equivalent to "KO" theory in low dimension if we only consider the 2-torsion. This is related to a question and an answer supports the claim. Here we denote the $p$-...
        6
        votes
        0answers
        143 views

        Arf-Brown-Kervaire invariant and a surjective map $G \to Pin^-$

        We know that the Arf-Brown-Kervaire (abk) invariant is a bordism invariant of $$ \Omega_2^{Pin^-}(pt)=\mathbb{Z}/(8\mathbb{Z}), $$ where the $\mathbb{Z}/(8\mathbb{Z})$ is generated by a 2-manifold $M^...
        5
        votes
        0answers
        56 views

        Triple data for Pontrjagin dual of the Spin bordism group

        It is said that the Pontrjagin dual of the 3-dimensional Spin bordism group of $BG$ for $G$ a finite group, $$ \text{Hom}(Ω^{spin}_3(BG),\mathbb{R/Z}), $$ can be expressed by triples of cochains $$(w, ...
        9
        votes
        1answer
        479 views

        The structure of complex cobordism cohomology of the Eilenberg-Maclane spectrum

        Let $MU$ be the complex bordism spectrum and let $H\mathbb{Z}$ be the Eilenberg-Maclane spectrum. Is it know what the structure of the complex cobordism cohomology $MU^{*}(H\mathbb{Z})$ is? EDIT: ...
        4
        votes
        0answers
        70 views

        Linear Independence & Integral Homology Cobordism Group

        The set of integral homology spheres up to integral homology cobordism forms an abelian group with the operation induced by the connected sum. This group is called integral homology cobordism group ...
        8
        votes
        0answers
        102 views

        Relating bordism generators in d and d+2 dimensions — an explicit example

        This is an attempt to make my relation between bordism invariants in $d$ and $d+2$ dimensions, following a previous attempt more explicit. This counts as a different question, since some more specific ...
        2
        votes
        1answer
        126 views

        Extending the maps between the bordism groups: NONE exsistence of a certain kind of extended group

        Let $M^d$ be a nontrivial bordism generator for the bordism group $$ \Omega_d^G= \mathbb{Z}_n, $$ suppose $G$ (like O, SO, Spin, etc) specify the group structure of the boridsm group. The $\mathbb{Z}...
        8
        votes
        0answers
        142 views

        “Gerbes” in the cobordism theory

        In a lecture I attended today, I heard the use of gerbes in the cobordism theory. Previously, I use cobordism theory, but I never encounter the term "gerbes" when I work on bordism or cobordism group ...
        4
        votes
        0answers
        67 views

        Relating bordism invairants in $d$ and $d+2$ dimensions

        Are there some relationship between mapping the bordism invairants of eq.1 and eq.2? $$\Omega_{O}^{d}(B(PSU(2^n)\rtimes\mathbb{Z}_2)) \tag{eq.1}$$ and $$\Omega_{O}^{d+2}(K(\mathbb{Z}/{2^n},2)) \...
        5
        votes
        1answer
        192 views

        Manifold generators of O-bordism invariants

        If I understand correctly, I can obtain the $O$-cobordism group of $$ \Omega^{O}_3(BO(3))=(\mathbb{Z}/2\mathbb{Z})^4, $$ The 3d cobordism invariants have 4 generators of mod 2 classes, are generated ...
        8
        votes
        2answers
        239 views

        Künneth formulas/theorem for bordism groups and cobordisms?

        We are familiar with Künneth theorem: The Kunneth formula is given by $R$ as a ring, $M,M'$ as the R-modules, $X,X'$ are some chain complex. The Kunneth formula shows the cohomology of a chain ...

        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>