$E_8 oplus m[1]$ ever diagonal?
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Let $E_8$ be the unique unimodular positive definite even integral symmetric form of rank 8. Let $[1]$ denote the unique unimodular positive definite even integral symmetric form of rank 1. Is $E_8 oplus m[1]$ ever diagonalizable for any $m geq 1$?
This question for me is motivated by thinking about intersection forms of 4-manifolds - hence the tag.
manifolds geometric-topology integer-lattices
asked Sep 6 at 5:05
user101010
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Let $E_8$ be the unique unimodular positive definite even integral symmetric form of rank 8. Let $[1]$ denote the unique unimodular positive definite even integral symmetric form of rank 1. Is $E_8 oplus m[1]$ ever diagonalizable for any $m geq 1$?
This question for me is motivated by thinking about intersection forms of 4-manifolds - hence the tag.
manifolds geometric-topology integer-lattices
asked Sep 6 at 5:05
user101010
1,706414
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Let $E_8$ be the unique unimodular positive definite even integral symmetric form of rank 8. Let $[1]$ denote the unique unimodular positive definite even integral symmetric form of rank 1. Is $E_8 oplus m[1]$ ever diagonalizable for any $m geq 1$?
This question for me is motivated by thinking about intersection forms of 4-manifolds - hence the tag.
manifolds geometric-topology integer-lattices
asked Sep 6 at 5:05
user101010
1,706414
Let $E_8$ be the unique unimodular positive definite even integral symmetric form of rank 8. Let $[1]$ denote the unique unimodular positive definite even integral symmetric form of rank 1. Is $E_8 oplus m[1]$ ever diagonalizable for any $m geq 1$?
This question for me is motivated by thinking about intersection forms of 4-manifolds - hence the tag.
manifolds geometric-topology integer-lattices
manifolds geometric-topology integer-lattices
asked Sep 6 at 5:05
user101010
1,706414
asked Sep 6 at 5:05
user101010
1,706414
asked Sep 6 at 5:05
user101010
1,706414
asked Sep 6 at 5:05
user101010
1,706414
asked Sep 6 at 5:05
user101010
1,706414
1,706414
add a comment |Â
add a comment |Â
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