Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following: C...
Transcript of Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following: C...
![Page 1: Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following: C 0 = C 1 = C 2 = C 3 = Z 0 = Explain your answer for.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1e5503460f94c35c76/html5/thumbnails/1.jpg)
Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following:
C0 =
C1 =
C2 =
C3 =
Z0 =
Explain your answer for Z0:
B0 =
H0 =
Rank C0 = Rank Z0 = Rank B0 = Rank H0 =
|C0| = |Z0| = |B0| = |H0|=
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![Page 2: Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following: C 0 = C 1 = C 2 = C 3 = Z 0 = Explain your answer for.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1e5503460f94c35c76/html5/thumbnails/2.jpg)
Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following:
Find the matrix for d0:
Find the matrix for d1:
Simplify the matrix for d1 so that the nonzero columns are linearly independent. Write the basis element above its corresponding column.
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![Page 3: Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following: C 0 = C 1 = C 2 = C 3 = Z 0 = Explain your answer for.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1e5503460f94c35c76/html5/thumbnails/3.jpg)
Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following:
Find the matrix for d2:
Simplify the matrix for d2 so that the nonzero columns are linearly independent. Write the basis element above its corresponding column.
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![Page 4: Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following: C 0 = C 1 = C 2 = C 3 = Z 0 = Explain your answer for.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1e5503460f94c35c76/html5/thumbnails/4.jpg)
Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following:
Z1 =
Explain your answer for Z1:
B1 =
H1 =
Rank C1 = Rank Z1 = Rank B1 = Rank H1 =
|C1| = |Z1| = |B1| = |H1|=
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![Page 5: Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following: C 0 = C 1 = C 2 = C 3 = Z 0 = Explain your answer for.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1e5503460f94c35c76/html5/thumbnails/5.jpg)
Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following:
Z2 =
Explain your answer for Z2:
B2 =
H2 =
Rank C2 = Rank Z2 = Rank B2 = Rank H2 =
|C2| = |Z2| = |B2| = |H2|=
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![Page 6: Let C be the simplicial complex on the right (the boundary of a tetrahedron). Find the following: C 0 = C 1 = C 2 = C 3 = Z 0 = Explain your answer for.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1e5503460f94c35c76/html5/thumbnails/6.jpg)
Barcode for H0
Barcode for H1