Calculate deRham Cohomology un R^3
I want to calculate the Cohomology groups of $B_r-B_s$ $(r>s)$ where $B_r$, $B_s$ are solid balls on $mathbb{R}^3$ and the boundary of $B_s$ is empty, I tried use Mayer Vietoris and the $U$,$V$ opens with $Ucap V$ are torus solid but it does not come to anything, in the books there are no examples of solids so if they have any advice I would appreciate it.
differential-geometry algebraic-topology
edited Dec 9 at 10:52
Tyrone
4,35011225
asked Dec 8 at 22:50
Kevin Alonso
72
|
show 2 more comments
I want to calculate the Cohomology groups of $B_r-B_s$ $(r>s)$ where $B_r$, $B_s$ are solid balls on $mathbb{R}^3$ and the boundary of $B_s$ is empty, I tried use Mayer Vietoris and the $U$,$V$ opens with $Ucap V$ are torus solid but it does not come to anything, in the books there are no examples of solids so if they have any advice I would appreciate it.
differential-geometry algebraic-topology
edited Dec 9 at 10:52
Tyrone
4,35011225
asked Dec 8 at 22:50
Kevin Alonso
72
Do they have same radius and center?
– Saucy O'Path
Dec 8 at 22:56
Doesn't $B_rsetminus B_s$ deformation retract onto the sphere of radius $t$ for $s<t<r$ ?
– Max
Dec 8 at 22:58
same center yeah, but the radius r is greater that s
– Kevin Alonso
Dec 8 at 23:00
Ah, ok. I thought $r$ and $s$ were the dimension for some reason.
– Saucy O'Path
Dec 8 at 23:01
No, they are un R^3, and the center is (0,0,0)
– Kevin Alonso
Dec 8 at 23:04
|
show 2 more comments
I want to calculate the Cohomology groups of $B_r-B_s$ $(r>s)$ where $B_r$, $B_s$ are solid balls on $mathbb{R}^3$ and the boundary of $B_s$ is empty, I tried use Mayer Vietoris and the $U$,$V$ opens with $Ucap V$ are torus solid but it does not come to anything, in the books there are no examples of solids so if they have any advice I would appreciate it.
differential-geometry algebraic-topology
edited Dec 9 at 10:52
Tyrone
4,35011225
asked Dec 8 at 22:50
Kevin Alonso
72
I want to calculate the Cohomology groups of $B_r-B_s$ $(r>s)$ where $B_r$, $B_s$ are solid balls on $mathbb{R}^3$ and the boundary of $B_s$ is empty, I tried use Mayer Vietoris and the $U$,$V$ opens with $Ucap V$ are torus solid but it does not come to anything, in the books there are no examples of solids so if they have any advice I would appreciate it.
differential-geometry algebraic-topology
differential-geometry algebraic-topology
edited Dec 9 at 10:52
Tyrone
4,35011225
asked Dec 8 at 22:50
Kevin Alonso
72
edited Dec 9 at 10:52
Tyrone
4,35011225
asked Dec 8 at 22:50
Kevin Alonso
72
edited Dec 9 at 10:52
Tyrone
4,35011225
edited Dec 9 at 10:52
Tyrone
4,35011225
edited Dec 9 at 10:52
Tyrone
4,35011225
4,35011225
asked Dec 8 at 22:50
Kevin Alonso
72
asked Dec 8 at 22:50
Kevin Alonso
72
asked Dec 8 at 22:50
Kevin Alonso
72
72
Do they have same radius and center?
– Saucy O'Path
Dec 8 at 22:56
Doesn't $B_rsetminus B_s$ deformation retract onto the sphere of radius $t$ for $s<t<r$ ?
– Max
Dec 8 at 22:58
same center yeah, but the radius r is greater that s
– Kevin Alonso
Dec 8 at 23:00
Ah, ok. I thought $r$ and $s$ were the dimension for some reason.
– Saucy O'Path
Dec 8 at 23:01
No, they are un R^3, and the center is (0,0,0)
– Kevin Alonso
Dec 8 at 23:04
|
show 2 more comments
Do they have same radius and center?
– Saucy O'Path
Dec 8 at 22:56
Doesn't $B_rsetminus B_s$ deformation retract onto the sphere of radius $t$ for $s<t<r$ ?
– Max
Dec 8 at 22:58
same center yeah, but the radius r is greater that s
– Kevin Alonso
Dec 8 at 23:00
Ah, ok. I thought $r$ and $s$ were the dimension for some reason.
– Saucy O'Path
Dec 8 at 23:01
No, they are un R^3, and the center is (0,0,0)
– Kevin Alonso
Dec 8 at 23:04
Do they have same radius and center?
– Saucy O'Path
Dec 8 at 22:56
Do they have same radius and center?
– Saucy O'Path
Dec 8 at 22:56
Doesn't $B_rsetminus B_s$ deformation retract onto the sphere of radius $t$ for $s<t<r$ ?
– Max
Dec 8 at 22:58
Doesn't $B_rsetminus B_s$ deformation retract onto the sphere of radius $t$ for $s<t<r$ ?
– Max
Dec 8 at 22:58
same center yeah, but the radius r is greater that s
– Kevin Alonso
Dec 8 at 23:00
same center yeah, but the radius r is greater that s
– Kevin Alonso
Dec 8 at 23:00
Ah, ok. I thought $r$ and $s$ were the dimension for some reason.
– Saucy O'Path
Dec 8 at 23:01
Ah, ok. I thought $r$ and $s$ were the dimension for some reason.
– Saucy O'Path
Dec 8 at 23:01
No, they are un R^3, and the center is (0,0,0)
– Kevin Alonso
Dec 8 at 23:04
No, they are un R^3, and the center is (0,0,0)
– Kevin Alonso
Dec 8 at 23:04
|
show 2 more comments
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Do they have same radius and center?
– Saucy O'Path
Dec 8 at 22:56
Doesn't $B_rsetminus B_s$ deformation retract onto the sphere of radius $t$ for $s<t<r$ ?
– Max
Dec 8 at 22:58
same center yeah, but the radius r is greater that s
– Kevin Alonso
Dec 8 at 23:00
Ah, ok. I thought $r$ and $s$ were the dimension for some reason.
– Saucy O'Path
Dec 8 at 23:01
No, they are un R^3, and the center is (0,0,0)
– Kevin Alonso
Dec 8 at 23:04