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David White
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Cobodism Cobordism/bodismbordism group based on orbifolds with corners

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Hao Yu
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We define a geometric homology group of a topological space $X$ as follows: the chain complex $C_{\bullet}$is freely generated by the maps $f$ from a compact oriented orbifold with corners $P$ to $X$, graded by the dimension of $P$, the boundary map from $C_n$ to $C_{n-1}$ is defined to be the restriction of $f$ to the (oriented)sum of its codimension $\ge$ 1 faces. If $X$ is itself a compact oriented orbifold with corners, is it true that the homology $H_{\bullet}(C, Q)$ over $Q$ is isomorphic to the rational singular homology group of $X$?

We define a geometric homology group of a topological space $X$ as follows: the chain complex $C_{\bullet}$is freely generated by the maps $f$ from a compact oriented orbifold with corners $P$ to $X$, graded by the dimension of $P$, the boundary map from $C_n$ to $C_{n-1}$ is defined to be the restriction of $f$ to the (oriented)sum of its codimension 1 faces. If $X$ is itself a compact oriented orbifold with corners, is it true that the homology $H_{\bullet}(C, Q)$ over $Q$ is isomorphic to the rational singular homology group of $X$?

We define a geometric homology group of a topological space $X$ as follows: the chain complex $C_{\bullet}$is freely generated by the maps $f$ from a compact oriented orbifold with corners $P$ to $X$, graded by the dimension of $P$, the boundary map from $C_n$ to $C_{n-1}$ is defined to be the restriction of $f$ to the (oriented)sum of its codimension $\ge$ 1 faces. If $X$ is itself a compact oriented orbifold with corners, is it true that the homology $H_{\bullet}(C, Q)$ over $Q$ is isomorphic to the rational singular homology group of $X$?

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Hao Yu
  • 781
  • 4
  • 13

We define a geometric homology group of a topological space $X$ as follows: the chain complex $C_{\bullet}$is freely generated by the maps $f$ from ana compact oriented orbifold with corners $P$ to $X$, graded by the degreedimension of $P$, the boundary map from $C_n$ to $C_{n-1}$ is defined to be the restriction of $f$ to the (oriented)sum of its codimension 1 faces. If $X$ is itself ana compact oriented orbifold with corners, is it true that the homology $H_{\bullet}(C, Q)$ over $Q$ is isomorphic to the rational singular homology group of $X$?

We define a geometric homology group of a topological space $X$ as follows: the chain complex $C_{\bullet}$is freely generated by the maps $f$ from an oriented orbifold with corners $P$ to $X$, graded by the degree of $P$, the boundary map from $C_n$ to $C_{n-1}$ is defined to be the restriction of $f$ to the (oriented)sum of its codimension 1 faces. If $X$ is itself an oriented orbifold with corners, is it true that the homology $H_{\bullet}(C, Q)$ over $Q$ is isomorphic to the rational singular homology group of $X$?

We define a geometric homology group of a topological space $X$ as follows: the chain complex $C_{\bullet}$is freely generated by the maps $f$ from a compact oriented orbifold with corners $P$ to $X$, graded by the dimension of $P$, the boundary map from $C_n$ to $C_{n-1}$ is defined to be the restriction of $f$ to the (oriented)sum of its codimension 1 faces. If $X$ is itself a compact oriented orbifold with corners, is it true that the homology $H_{\bullet}(C, Q)$ over $Q$ is isomorphic to the rational singular homology group of $X$?

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Hao Yu
  • 781
  • 4
  • 13
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